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**More than One Correct Options**

**Ques 1: particle having a velocity v = v _{0} at t = 0 is decelerated at the rate where Î± is a positive constant.(a) The particle comes to rest at **

i.e., the particle will stop at

Option (a) is correct.

Option (b) is incorrect.

From Eq. (i),

or

or

âˆ´

i.e., when the particle stops

Option (d) is correct.

Option (c) is incorrect.

or

At t = 0, v = 16 m/s

âˆ´ â€¦(i)

From above relation v is zero at t = 8 s

Options (a) is correct.

From relation (i),

âˆ´

i.e.,

[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)

Distance travelled in 10 s

= s8 + (s

= 94 m

Option (c) is correct.

Velocity of particle at t = 10 s

âˆ´Speed of particle at t = 10 s is 9 m/s.

Option (d) is correct.

âˆ´ Option (a) is incorrect.

âˆ´ Option (b) is correct.

v

âˆ´ Option (c) is incorrect.

âˆ´

âˆ´ Option (d) is incorrect.

(a) Velocity of A relative to B is

(b) Position of A relative to B as a function of time is given by

(c) Velocity of A relative to B is

(d) Position of A relative to B as a function of time is given by

Option (a) is correct.

Option (c) is incorrect.

At any time

Position of A relative to B:

Option (b) is correct.

Option (d) is incorrect.

Combining Eqs. (i) and (ii),

2s

Option (d) is correct.

i.e.,

In Case II.

i.e.,

Option (a) is correct.

Option (b) is incorrect.

Also if particleâ€™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).

âˆ´ Options (b) and (c) are correct.

and options (a) and (d) are incorrect.

â‡’ ma = Î± t

or â€¦(i)

âˆ´ Graph between a (acceleration) and time (t) will be as curve 1.

âˆ´ Option (a) is correct.

From equation

âˆ´

i.e.,

âˆ´ Graph between velocity (v) and time (t) will be as curve 2.

Option (b) is correct.

or

or

or â€¦(i)

[C

Substituting s = 10 m in Eq. (i),

i.e., v = 10 m/s

âˆ´ Option (b) is correct.

From Eq. (i) v to be maximum

- s + 30 = 0

s = 30**Ques 9: For a moving particle which of the following options may be correct?****Ans: **(a, c)**Sol: **If particleâ€™s path is

(i) straight with backward motion

(ii) not straight somewhere.

Distance moved will be greater than the modulus of displacement

âˆ´

Option (a) is correct.

If particle returns to its initial position, the value of will be zero while its average speed (v_{av}) will not be zero.

âˆ´ Option (c) is correct.**Ques 10: Identify the correct graph representing the motion of a particle along a straight line with constant acceleration.****Ans: (a, d)****Sol:** If u = 0, v = at and

âˆ´ 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 (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**

if v sin Î¸ = u

i.e., v > u

Option (c) is correct.

Time to cross the river

Option (b) is correct.

Option (a) is correct.

Option (a) is correct.

As slope v-t is same throughout, particleâ€™s acceleration is constant.

Option (b) is correct.

As net area under the curve is zero.

displacement of particle at time 2T is zero.

Option (c) is correct.

Option (d) is correct.**Ques 13: The speed of a train increases at Î± constant rate a from zero to v and then remains constant for an interval and finally decreases to zero at a constant rate Î². The total distance travelled by the train is l. The time taken to complete the journey is t. Then****Ans: **(b, d)**Sol:**

Option (b) is correct.

For t to be minimum.

or

or

Option (d) is correct.**Ques 14: A particle moves in x-y plane and at time t is at the point (t ^{2}, t^{3} - 2t), then which of the following is/are correct? **

âˆ´ at t = 0 particle is moving parallel to y-axis.

Option (a) is correct.

Option (d) is incorrect.

At t = 0,

and

At t = 0,

i.e.,

Option (b) is correct.

âˆ´ Particle is moving parallel to x-axis.

Option (c) is correct.

âˆ´ v = 5a t

or v = 10 m/s

Option (a) is correct.

Time t to reach P from T

10 = 2 + at

â‡’ â€¦(i)

Time t' to reach Y from P

14 = 10 + at'

âˆ´ â€¦(ii)

Comparing Eq. (i) and Eq. (ii),

t = 2t'

Option (c) is correct.

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