Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev

DC Pandey (Questions & Solutions) of Physics: NEET

NEET : Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev

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More than One Correct Options

Ques 1: particle having a velocity v = v0 at t = 0 is decelerated at the rate Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev where α is a positive constant.
(a) The particle comes to rest at Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev

(b) The particle will come to rest at infinity.
(c) The distance travelled by the particle before coming to rest is Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
(d) The distance travelled by the particle before coming to rest is Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Ans: (a, d)
Sol: ∵ Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev     …(i)
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
i.e., the particle will stop at
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (a) is correct.
Option (b) is incorrect.
From Eq. (i),
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
or Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
or Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
i.e., when the particle stops
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (d) is correct.
Option (c) is incorrect.

Ques 2: At time t = 0, a car moving along a straight line has a velocity of 16 ms-1. It slows down with an acceleration of - 0.5t ms-2, where t is in second. Mark the correct statement (s). 
(a) The direction of velocity changes at t = 8 s 
(b) The distance travelled in 4 s is approximately 58.67 m 
(c) The distance travelled by the particle in 10 s is 94 m 
(d) The speed of particle at t = 10 s is 9 ms-1
Ans: (all)
Sol: a = - 0.5 t (m/s2)
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
or Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
At t = 0, v = 16 m/s
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev …(i)
From above relation v is zero at t = 8 s
Options (a) is correct.
From relation (i),
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
i.e., Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev [As at t = 0, s = 0]
At t = 4 s
s = 58.67 m
Option (b) is correct.
The particle returns back at t = 8 s
From relation (ii)
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Distance travelled in 10 s
= s8 + (s8 - s10) = (2 x 85.33 ) - 76.66
= 94 m
Option (c) is correct.
Velocity of particle at t = 10 s
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴Speed of particle at t = 10 s is 9 m/s.
Option (d) is correct.

Ques 3: An object moves with constant acceleration Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev Which of the following expressions are also constant ?
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Ans: (b)
Sol: Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴ Option (a) is incorrect.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴ Option (b) is correct.
v2 is scalar.
∴ Option (c) is incorrect.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴ Option (d) is incorrect.

Ques 4: Ship A is located 4 km north and 3 km east of ship B. Ship A has a velocity of 20 kmh-1 towards the south and ship B is moving at 40 kmh-1 in a direction 37° north of east. X and 7-axes are along east and north directions, respectively
(a) Velocity of A relative to B is Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
(b) Position of A relative to B as a function of time is given by
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
(c) Velocity of A relative to B is Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
(d) Position of A relative to B as a function of time is given by Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ans: (a, b)
Sol:
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (a) is correct.
Option (c) is incorrect.
At any time
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Position of A relative to B:
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (b) is correct.
Option (d) is incorrect.

Ques 5: Starting from rest a particle is first accelerated for time t1 with constant acceleration a1 and then stops in time t2 with constant retardation a2. Let v1 be the average velocity in this case and s1 the total displacement. In the second case it is accelerating for the same time tx with constant acceleration 2a1 and come to rest with constant retardation a2 in time t3. If v2 is the average velocity in this case and s2 the total displacement, then 
(a) v2 = 2v1 
(b) 2v1 < v2 < 4v1 
(c) s2 = 2s1 
(d) 2s1 <s< 4s1
Ans: (a, d)
Sol: Case I.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Case II.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev  …(i)
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev   …(ii)
Combining Eqs. (i) and (ii),
2s1 < s2 < 4s1 
Option (d) is correct.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
i.e., Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
In Case II.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
i.e., Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (a) is correct.
Option (b) is incorrect.

Ques 6: A particle is moving along a straight line. The displacement of the particle becomes zero in a certain time (t > 0) The particle does not undergo any collision. 
(a) The acceleration of the particle may be zero always 
(b) The acceleration of the particle may be uniform 
(c) The velocity of the particle must be zero at some instant 
(d) The acceleration of the particle must change its direction
Ans: (b, c)
Sol: If the particle’s initial velocity is + ive and has some constant - ive acceleration the particle will stop somewhere and then return back to have zero displacement at same time t (> 0).
Also if particle’s initial velocity is - ive and has some constant + ive acceleration the particle will stop somewhere and then return back to have zero displacement at same time t (> 0).
∴ Options (b) and (c) are correct.
and options (a) and (d) are incorrect.

Ques 7: A particle is resting over a smooth horizontal floor. At t = Q a horizontal force starts acting on it. Magnitude of the force increases with time according to law F = at, where a is a positive constant. From figure, which of the following statements are correct ? 
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
(a) Curve 1 can be the plot of acceleration against time 
(b ) Curve 2 can be the plot of velocity against time 
(c) Curve 2 can be the plot of velocity against acceleration 
(d) Curve 1 can be the plot of displacement against time
Ans: (a, b)
Sol: F = α t
⇒ ma = α t
or  Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev   …(i)
∴ Graph between a (acceleration) and time (t) will be as curve 1.
∴ Option (a) is correct.
From equation
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
i.e., Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴ Graph between velocity (v) and time (t)  will be as curve 2.
Option (b) is correct.

Ques 8: A train starts from rest at S = 0 and is subjected to acceleration as shown 
(a) velocity at the end of 10 m displacement is 20 ms-1 
(b) velocity of the train at S = 10m is 10 ms-1 
(c) The maxim um velocity attained b y train is Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
(d) The maximum velocity attained by the train is 15 ms-1
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Ans: (b, c)
Sol:
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
or Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
or Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
or Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev  …(i)
[C1 = 0 as at s = 0 particle is at rest]
Substituting s = 10 m in Eq. (i),
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
i.e.,   v = 10 m/s
∴ Option (b) is correct.

From Eq. (i) v to be maximum
- s + 30 = 0
s = 30
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev

Ques 9: For a moving particle which of the following options may be correct?
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Ans: (a, c)
Sol: If particle’s path is
(i) straight with backward motion
(ii) not straight somewhere.
Distance moved will be greater than the modulus of displacement
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (a) is correct.
If particle returns to its initial position, the value of  Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev will be zero while its average speed (vav) will not be zero.
∴ Option (c) is correct.

Ques 10: Identify the correct graph representing the motion of a particle along a straight line with constant acceleration.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Ans: (a, d)
Sol: If u = 0, v = at and Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴  v-t graph will be as shown in (a).
s-t graph will be as shown in (d).

Ques 11: A man who can swim at a velocity v relative to water wants to cross a river of width b, flowing with a speed u.
(a) The minimum time in which he can cross the river is b/v
(b) He can reach a point exactly opposite on the bank in time Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
(c) He cannot reach the point exactly opposite on the bank if u > v
(d) He cannot reach the point exactly opposite on the bank if v > u

Ans: (a, b, c)
Sol: Swimmer will reach point B
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
if  v sin θ = u
i.e., v > u
Option (c) is correct.
Time to cross the river
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (b) is correct.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (a) is correct.

Ques 12: The figure shows the velocity (v) of a particle plotted against time (t).
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev 
(a) The particle changes its direction of motion at some points 
(b) The acceleration of the particle remains constant 
(c) The displacement of the particle is zero 
(d) The initial and final speeds of the particle are the same
Ans: (all)
Sol: At time T, particle’s velocity change from –ive to + ive.
Option (a) is correct.
As slope v-t is same throughout, particle’s acceleration is constant.
Option (b) is correct.
As net area under the curve is zero.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev displacement of particle at time 2T is zero.
Option (c) is correct.

Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (d) is correct.

Ques 13: The speed of a train increases at α constant rate a from zero to v and then remains constant for an interval and finally decreases to zero at a constant rate β. The total distance travelled by the train is l. The time taken to complete the journey is t. Then
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Ans: (b, d)
Sol:
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (b) is correct.
For t to be minimum.

Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
or Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
or Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (d) is correct.

Ques 14: A particle moves in x-y plane and at time t is at the point (t2, t3 - 2t), then which of the following is/are correct? 
(a) At t = 0, particle is moving parallel to y-axis 
(b) At t = 0, direction of velocity and acceleration are perpendicular.
(c) Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev particle is moving parallel to x-axis.
(d) At t = 0, particle is at rest.
Ans: (a, b, c)
Sol: 
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴ at t = 0 particle is moving parallel to y-axis.
Option (a) is correct.
Option (d) is incorrect.
At t = 0,  Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
and Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
At t = 0, Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
i.e.,  Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Option (b) is correct.
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev 
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴ Particle is moving parallel to x-axis.
Option (c) is correct.

Ques 15: A car is moving with uniform acceleration along a straight line between two stops X and Y. Its speed at X and 7 are 2 ms-1 and 14 ms-1, Then 
(a) its speed at mid-point of X Y is 10 ms-1 
(b) its speed at a point A such that XA : AY = 1 : 3 is 5 ms-1 
(c) the time to go from X to the mid-point of X Y is double o f that to go from mid-point to Y 
(d) the distance travelled in first half of the total time is half of the distance travelled in the second half of the time
Ans: (a, c)
Sol: 
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev
∴ v = 5a t1 
or    v = 10 m/s
Option (a) is correct.
Time t to reach P from T
10 = 2 + at
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev  …(i)
Time t' to reach Y from P
14 = 10 + at'
Motion in One Dimension: JEE Advance(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev  …(ii)
Comparing Eq. (i) and Eq. (ii),
t = 2t'
Option (c) is correct.

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