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All questions of Motion in a Straight Line for JEE Exam

The ratio of magnitude of velocity and speed is always:
  • a)
    Equal to or less than one
  • b)
    Less than one
  • c)
    One
  • d)
    Equal to or greater than one
Correct answer is option 'A'. Can you explain this answer?

Anjana Sharma answered
The displacement of the body in given time is always equal to or less than distance covered, because, velocity is displacement per unit time and speed is distance covered per unit time, therefore, ratio of magnitude of velocity and speed is always equal to or less than one.

Which of the following is not an example of a rectilinear motion?
  • a)
    A car moving on a straight road.
  • b)
    A rain drop falling towards the earth.
  • c)
    A car moving in a circular path.
  • d)
    A wooden block sliding down the inclined plane.
Correct answer is option 'A'. Can you explain this answer?

Neha Joshi answered
Rectilinear motion is another name for straight-line motion
A body is said to experience rectilinear motion if any two particles of the body travel the same distance along two parallel straight lines.
A car moving in a circular path changes its direction at every instant. Thus, it is not the rectilinear motion.

A particle is moving along a circle of radius R such that it completes one revolution in 40 seconds. What will be the displacement after 2 minutes 20 seconds?
  • a)
    6R
  • b)
    2R
  • c)
    4R
  • d)
    R
Correct answer is option 'B'. Can you explain this answer?

Nandini Patel answered
1 revolution in 40 seconds
In 1 second it covers = 1/40 revolution
In 140 sec = 1/40 * 140 =7/2 rotation = 3 and half rotation
Then the particle will be on the diametrically opposite end. 
Therefore, Displacement = R + R = 2R

Two stones of different masses are thrown vertically upward with same initial velocity. Which one will rise to a greater height ?
  • a)
    Stone of lower mass
  • b)
    Stone of higher mass
  • c)
    Both will rise to the same height
  • d)
    Information given is insufficient
Correct answer is option 'C'. Can you explain this answer?

Neha Joshi answered
If we write the equation of motion for both the masses and derive a simple equation to find the maximum vertical height let say H, we get for any particle for some mass m,
H = v2 / 2a
Where a is gravitational acceleration and v is vertical speed. Thus as H does not depend upon m, we get both particles would have equal maximum height.

A truck has a velocity of 2 m /s at time t=0. It accelerates at 2 m / s2 on seeing police .What is its velocity in m/s at a time of 2 sec
  • a)
    6
  • b)
    7
  • c)
    3
  • d)
    4
Correct answer is option 'A'. Can you explain this answer?

Naina Sharma answered
Explanation:
Initial velocity u = 2 m/s
final velocity = v m/s
Time duration = final time - initial time = 2-0 = 2 s
acceleration a = 2 m/s​​​​​​2
We know,
v = u + at
=> v = 2+2x2
=> v = 6 m/s

 The numerical ratio of velocity to speed is:
  • a)
    Either less than or equal to 1
  • b)
    Equal to 1
  • c)
    Greater than 1
  • d)
    Less than 1
Correct answer is option 'A'. Can you explain this answer?

Charvi Mehta answered
When an object is moving along a straight path, magnitude of average velocity is equal to the average speed. Therefore, numerical ratio of average velocity to average speed is one in a straight line motion.
But, during curved motion, the displacement<distance covered, so the velocity<speed.

A vehicle travels half the distance L with speed V1and the other half with speed V2, then its average speed is
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?

Gaurav Kumar answered

 
Let the vehicle travels from A to B. Distances, velocities, and time taken are shown. To calculate average speed we will calculate the total distance covered and will divide it by the time interval in which it covers that total distance. 
Time taken to travel first half distance t1
Time taken to travel first half distance t1
Total time taken = t+ t2
We know that vav ​= Average speed = Total Distance / Total Time
 

A ball is thrown vertically upward. At the highest point in its path, which of the following statements is correct?
  • a)
    The velocity is zero and the acceleration is pointing down
  • b)
    The velocity and acceleration are both zero
  • c)
    The acceleration is zero and the velocity is pointing up
  • d)
    The acceleration is zero and the velocity is pointing down
Correct answer is option 'A'. Can you explain this answer?

Geetika Shah answered
Until and unless the velocity of any object comes to zero, any peek in its displacement-time graph can’t be achieved. Which means for the height to be maximised the velocity must become zero. And any time of this motion the acceleration is always a constant downward due to gravity.

The ratio of displacement to distance is
  • a)
    Greater than 1
  • b)
    Either less than or equal to 1
  • c)
    Less than 1
  • d)
    Equal to 1
Correct answer is option 'B'. Can you explain this answer?

Saumya Dey answered
Ratio of Displacement to Distance

Displacement and distance are two terms used in physics to describe the motion of an object. Displacement refers to the change in position of an object from its initial to final position, whereas distance refers to the total path covered by the object during its motion.

Ratio of Displacement to Distance Formula

The ratio of displacement to distance is given by:

Displacement / Distance

This ratio is used to determine the efficiency of an object's motion. If the ratio is equal to 1, it means that the object has moved in a straight line from its initial to final position. If the ratio is less than 1, it means that the object has taken a longer path to reach its final position, and if the ratio is greater than 1, it means that the object has moved back and forth before reaching its final position.

Answer Explanation

The correct answer to the question is option B, which states that the ratio of displacement to distance is either less than or equal to 1. This is because an object can never cover a greater distance than its displacement. The displacement represents the shortest distance between the initial and final positions of an object, whereas the distance represents the total path covered by the object.

Therefore, the displacement can be equal to or less than the distance covered by the object, but it can never be greater than the distance. This is the reason why the ratio of displacement to distance is either less than or equal to 1.

The displacement of a particle starting from rest (at t = 0) is given by s = 6t2-t. The time in seconds at which the particle will attain zero velocity again, is
  • a)
    6
  • b)
    4
  • c)
    2
  • d)
    8
Correct answer is option 'B'. Can you explain this answer?

Preeti Iyer answered
v = ds/dt
v = 12t - 3t2
0 = 3t (4 - t)
⇒ t = 0 or 4
Here t = 0 is not realistic so at t = 4 the velocity will be zero.
Thus, the particle will attain zero velocity at the time of 4 seconds.

If a moving body comes to rest, then its acceleration is______.
  • a)
    Positive
  • b)
    Both of these depending upon the initial velocity
  • c)
    Constant
  • d)
    Negative
Correct answer is option 'D'. Can you explain this answer?

But, I think it should be (c) because: it was initially moving with a speed and then, it came to rest. 

So, the speed must decrease with time to become 0m/s (to become at rest). so, the acceleration must be negative so that it can decrease with time ( as the change in velocity will become negative only when the speed decreases). 

So, I think the answer is (C)

Please correct me if I am wrong🤔

If the position- time graph is a straight line parallel to the time axis
  • a)
    The velocity is zero
  • b)
    The velocity is decreasing
  • c)
    The velocity is increasing
  • d)
    The velocity is constant but non zero
Correct answer is option 'A'. Can you explain this answer?

Neha Sharma answered
Explanation:Position-time graph of horizontal straight line parallel to time axis represents that the position of the body does not changes with the passage of time. So it represents the rest state of motion.It means velocity of object is zero.

A car moving with a speed of 50 km/h, can be stopped by brakes after at least 6m. If the same car is moving at a speed of 100 km/h, the minimum stopping distance is               [AIEEE 2003]
  • a)
    12 m 
  • b)
     18 m
  • c)
     24 m
  • d)
    6 m
Correct answer is option 'C'. Can you explain this answer?

Hansa Sharma answered
We know that retardation of a car with an initial speed of 50kmph stops after 6 m.
We know that v2 - u2 = 2as  (third equation of motion)
► 0 - 502 = 2 * a * 6
► a = - 502 / 12
Hence when the initial speed is 100 kmph
We get,
► -1002 = 2 * a * s
► 2 * s = 12 * (1002 / 502)
Thus we get s = 24 m.

Two balls of equal mass and of Perfectly inelastic material are lying on the floor. One of the balls with velocity V is made to strike the second ball. Both the balls after impact will move with a velocity
  • a)
    v
  • b)
    v/8
  • c)
    v/4
  • d)
    v/2
Correct answer is option 'D'. Can you explain this answer?

Neha Joshi answered
Given:
Let two balls A and B have mass mA, mB respectively, and their initial velocities are uA and uB. After the collision, they will move with the same velocity, vo
Given that mass of both balls are same.
So  mA = mB = m
uA = V,  uB = 0
From the Concept of Momentum Conservation:
mAuA + mBuB = (m+m)vo
mV = 2mvo
vo = V/2
Both the balls after impact will move with velocity v/2.

An object is said to be in uniform motion in a straight line if its displacement
  • a)
    is decreasing in equal intervals of time
  • b)
    is increasing in equal intervals of time
  • c)
    is equal in equal intervals of time.
  • d)
    is equal in not equal intervals of time.
Correct answer is option 'C'. Can you explain this answer?

Mira Joshi answered
Explanation:Uniform motion is the kind of motion in which a body covers equal displacement in equal intervals of time. It does not matter how small the time intervals are, as long as the displacements covered are equal.
If a body is involved in rectilinear motion and the motion is uniform, then the acceleration of the body must be zero.

A boy throws a ball up and catches it when the ball falls back. In which part of the motion the ball is accelerating?
  • a)
    During downward motion
  • b)
    When the ball comes to rest
  • c)
    During upward motion
  • d)
    When the boy catches the ball
Correct answer is 'A'. Can you explain this answer?

Hansa Sharma answered
  • When the ball moves upward, the force of gravitation is acting in the opposite direction of the ball that is why in that case acceleration is negative or in other words deceleration takes place.
  • But when the ball is moving downwards the force of gravitation is in the same direction of the motion of the ball thus acceleration takes place in this case.

The ratio of C.G.S. to M.K.S. unit of acceleration is:​
  • a)
    1:10
  • b)
    1:1
  • c)
    1:100
  • d)
    10:1
Correct answer is 'C'. Can you explain this answer?

Vikram Khanna answered
M.K.S. unit of acceleration = 1m/^s2
C.G.S unit of acceleration/ M,K.S unit of acceleration =
1cm/^s2 / 1m/^s2
= 1cm / 100 cm
= 1/100
=1:100

The S.I. unit of acceleration is:​
  • a)
     ms2
  • b)
    ms
  • c)
    ms-2
  • d)
    m
Correct answer is option 'C'. Can you explain this answer?

Calculating acceleration involves dividing  velocity by time  Or we can say,  dividing the meter per second by the second. i.e.
[ m/s2 = m/s / s  ] 
Therefore, option ( c) ms-2 is the  correct answer.

Acceleration is defined as the rate of change of:
  • a)
    Distance
  • b)
    Velocity
  • c)
    Speed
  • d)
    Displacement
Correct answer is option 'B'. Can you explain this answer?

Anita Menon answered
Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.

Speed time graph of a particle moving along a fixed direction is shown in the figure below. The average speed of the particle over the interval: t = 0 s to 10 s.
  • a)
    16 m/s
  • b)
    6 m/s
  • c)
    10 m/s
  • d)
    0.6 m/s
Correct answer is option 'B'. Can you explain this answer?

Om Desai answered
From the given graph we get that the area of the given graph is total distance covered that is 
=  ½ x 10 x 12
=  60m
And total time taken is 10 sec
Thus average speed is  60m / 10sec
 = 6 m/s

Two trains are each 50 m long moving parallel to each other at speeds 10 m/s and 15 m/s respectively, at what time will they pass each other?  
  • a)
    8 s  
  • b)
    4 s  
  • c)
    2 s  
  • d)
    6 s 
Correct answer is option 'B'. Can you explain this answer?

Preeti Iyer answered
 As both the trains are moving in the opposite direction, the relative speed of each train with respect to each other be, v=10+15=25m/s
Here distance covered by each train = sum of their lengths =50+50=100m
∴ Required time=100/25​=4sec

Choose the correct option:
  • a)
    distance is a scalar, velocity is a vector , acceleration is a vector.
  • b)
    distance is a vector, velocity is a scalar, acceleration is a vector.
  • c)
    distance is a vector, velocity is a vector, acceleration is a vector.
  • d)
    distance is a scalar, velocity is a vector, acceleration is a scalar.
Correct answer is 'A'. Can you explain this answer?

Raghav Bansal answered
  • Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. 
  • Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity.
  • Velocity is a vector quantity that refers to the speed of an object in a particular direction.

If a body losses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest ?                             [AIEEE 2002]
  • a)
    1 cm 
  • b)
    2cm
  • c)
    3cm
  • d)
    4cm
Correct answer is option 'A'. Can you explain this answer?

Ayush Joshi answered
Let the initial velocity of the body be u. Its velocity becomes u/2 after penetrating 3 cm in the block. We can calculate the deceleration of the body using these.
v2= u2 +2as
u2/4 = u2 + 2ax3
-3u2/4 = 6a
a = -u2/8
Now, we can calculate the distance the body travels till it comes to rest.
v2 = u2 + 2as
0 = u2 +2x(-u2/8)xs
u2 = u2s/4
s = 4 cm
Therefore, the body penetrates 1 cm (4-3=1cm) more before coming to rest.
I hope you understand the concept.

The kinematic equation of motion v = u+at is not applicable if :
  • a)
    Displacement is not constant
  • b)
    motion is non-uniform.
  • c)
    acceleration is not constant
  • d)
    velocity is not constant
Correct answer is option 'C'. Can you explain this answer?

Yash Ghoshal answered
Explanation:

The kinematic equation of motion v = u + at is one of the four equations of motion which are used to describe the motion of an object under constant acceleration. The equation shows the relationship between the initial velocity (u), acceleration (a), time (t), and final velocity (v) of an object. However, this equation is not applicable if the acceleration is not constant.

Constant acceleration means that the rate of change of velocity is constant. If the acceleration is not constant, then the rate of change of velocity is changing, and the equation v = u + at does not hold true for the entire motion.

For example, if an object is moving in a circular path, its acceleration changes direction at every point, and hence, the acceleration is not constant. In this case, the kinematic equation cannot be used to describe the motion of the object.

Similarly, if an object is thrown vertically upwards, the acceleration of the object changes as it moves upwards and then downwards due to the force of gravity. Hence, the kinematic equation v = u + at cannot be used to describe the entire motion of the object.

Conclusion:

In conclusion, the kinematic equation of motion v = u + at is not applicable if the acceleration is not constant, and the rate of change of velocity is changing. The equation is valid only for objects that are moving under constant acceleration. Hence, before using this equation to solve any problem, it is important to check whether the acceleration is constant or not.

Slope of displacement time graph or x-t graph gives us the particles’ ____________.
  • a)
    displacement
  • b)
    deceleration
  • c)
    velocity
  • d)
    acceleration
Correct answer is option 'C'. Can you explain this answer?

Rahul Bansal answered
Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s) or as the SI base unit of (m⋅s−1).

An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e. 120 km/h, the stopping distance will be                         [AIEEE 2004]
  • a)
    20 m
  • b)
    40 m
  • c)
    60m 
  • d)
    80 m
Correct answer is option 'D'. Can you explain this answer?

Mira Sharma answered
The initial speed of the car in 1st case = 60kmph = 50/3 m/s
Final speed  = 0
Let the deceleration be a
We have
(0)^2  - (50/3)^2 = 2ax(20)
=>a = -(50/3)^2/40 = - 6.94 ms^-2 (approx)
Considering the acceleration to be same in both case
The initial speed at the second case = 120kmph=100/3 m/s
Let the distance be x
Final speed = 0
We have
v^2-u^2 =2ax
=>0^2 – (100/3)^2 =2x (-6.94)x
=>x = 80 m

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