Motion in a Straight Line Important Extra Questions Very Short Answer Type
Can a moving body have relative velocity zero with respect to another body? Give an example.
Yes, two trains running on two parallel tracks with the same velocity in the same direction.
Can there be motion in two dimensions with acceleration in only one dimension?
Yes, projectile motion.
Is it true that a body is always at rest in a frame that is fixed to the body itself?
Tell under what condition a body moving with uniform velocity can be in equilibrium?
When the net force on the body is zero.
What does the speedometer records: the average speed or the instantaneous speed?
It records (or measures) the instantaneous speed.
Can an object be accelerated without speeding up or slowing down? Give examples,
Yes, circular motion.
Is it possible to have the rate of change of velocity constant while the velocity itself changes both in magnitude and direction? Give an example.
Yes, in projectile motion.
Which motion is exactly represented by Δs = vΔt?
It Represents motion with uniform velocity.
In which frame of reference is the body always at rest?
The body is always at rest in the frame attached to it i. e. inertial frame of reference.
What is common between the two graphs shown in figs, (a) and (b)?
Both these graphs represent that the velocity is negative.
What is common between the two graphs shown in figs, (a) and (b)?
Both these graphs represent that velocity is positive.
What is meant by a point object in Physics?
An object is said to be a point object if its dimensions are very small as compared to the distance covered by it.
The displacement of a body is zero. Is the distance covered by it is necessarily zero?
Which of the velocity or speed is measured by the speedometer of a vehicle?
Can you think of a situation where a body falling under gravity has constant velocity? Give example.
Yes, the terminal velocity of a body.
Give an example of a motion which even though is accelerated motion yet it is called uniform motion.
Uniform circular motion.
How many-dimensional motion does the following have?
(a) Train moving fast on its track.
One dimensional motion.
(b) A lizard moving on a wall in a room.
(c) Kite flying in the sky.
(d) Bee flying in a closed room.
When is the average velocity over an interval of time becomes equal to instantaneous velocity?
When the velocity is constant.
A coolie carries a bag of luggage from one side of a platform to another side on the same platform. How far vertically the load is shifted?
The displacement of a body is proportional to the square of time along a straight line. Is the body moving with constant velocity or constant acceleration?
It is moving with constant acceleration.
When the train in which you are sitting starts moving by the side of another train without jerks, you find that the other train is moving but when you look to the platform you find that your train is moving. Name the phenomenon responsible for such a motion.
Relative velocity is the phenomenon responsible for such a motion.
Under what condition the magnitude of the average velocity of a particle is equal to the average speed?
The magnitude of the average velocity of a particle is equal to the average speed if it moves with constant velocity.
Two particles A and B are moving along the same straight line with B being ahead of A. Velocities remaining unchanged, what would be the effect on the magnitude of relative velocity if A is ahead of B? ’
The magnitude of the relative velocity will remain the same i.e. no effect on its magnitude.
Define the speed of the object.
The speed of an object is defined as the distance covered by it per unit of time.
Why the speed of an object cannot be negative?
The speed of an object cannot be negative because the distance can never be negative.
Can a body have zero velocity and still accelerating?
Can the direction of the velocity of a body change, when acceleration is constant?
Is the acceleration of a car is greater when the accelerator is pushed to the floor or when the brake pedal is pushed hard?
The acceleration of the car is greater when the brake pedal is pushed hard because the car comes to rest suddenly i. e. the rate of change of velocity of the car is large in this case, so the acceleration.
The displacement is given by x = 2 + 4t + 5t2. Find the value of instantaneous acceleration.
a = d2x/dt2 = 10
A stone is thrown vertically upwards from the surface of Earth. What is the direction of the velocity and acceleration of the stone?
(a) on its upward motion
Velocity is vertically upward and acceleration is vertically downward.
(b) on its downward motion?
Both velocity and acceleration are vertically downward.
Can Earth be regarded as a point object if only the orbital motion of Earth around the Sun is considered? Why?
Yes. This is because the size of Earth is very small as compared to the size of the orbit of the Earth around the Sun.
The motion of two persons is shown by two straight lines on a displacement time graph intersecting each other at a certain point. What information do you get from the point of intersection?
This means that the two persons cross each other at a certain place at a given instant of time.
Following two equations represents the x – t relation for the motion of an objects.
x (t) = x(0) + v(0)t + 1/2 at2
and x(t) = v(0)t + 1/2 at2
What is the difference between them?
The first equation is a more general form of motion as it contains information regarding the initial position of the object.
Can the speed of a body change if its velocity is constant? Why?
No, the speed of a body cannot change if its velocity is constant which means that both the magnitude and direction of velocity do not change. The magnitude of velocity is speed, so speed cannot change.
If the instantaneous velocity of a particle is zero, will its instantaneous acceleration be necessarily zero?
What is the shape of the displacement time graph of a particle having an average velocity equal to its instantaneous velocity?
In this case, the velocity is uniform, so the x – t graph is a straight line.
Can there be a two-dimensional motion with acceleration in one dimension only? Give example.
Yes, a projectile motion which is two-dimensional one has acceleration only in one dimension i.e. vertically downward.
Under what condition will the distance and displacement of a moving object will have the same magnitude?
The distance and displacement of a moving object will have the same magnitude when it is moving with uniform velocity along a straight line.
Under what condition an object in motion cannot be considered a point object?
A moving object cannot be considered as a point object if its size is not negligible as compared to the distance travelled by it.
Define a point object.
It is defined as an object having dimensions (length, breadth, thickness etc.) very small as compared to the distance covered by it.
Is the following graph possible for the motion of a particle moving along a straight line?
Explain why the graph in the above question is not possible?
This is because the speed for a given time is negative and speed is always positive.
Why the following graph is not possible for the motion of a particle moving along a straight line?
This is because here the path length decreases with time while it must either increase or must remain constant.
What happens to kinematic equations under time reversal?
The kinematic equations of motion don’t change in the form under time reversal i.e. if t is replaced by -t.
What happens to the uniform motion of a body when it is given an acceleration at right angles to its motion?
The body will come in a circular motion when it is given an acceleration at right angles to its motion.
To deal with physical phenomena, we consider objects even as big as Sun a point objects. Can you name physical phenomena in which Earth cannot be taken as a point object?
The occurrence of solar or lunar eclipse does not allow Earth to be taken as a point object otherwise the phenomena cannot be explained.
The average velocity of a body moving with uniform acceleration is given by 1/2 (u + v). Ii the acceleration changes from point to point can the average velocity be still given by this expression? Give reason.
No, the average velocity cannot be given by 1/2 (u + v) in case the acceleration varies from point to point i.e. if it is not uniform. This is because the slope of the v-t graph does not remain the same at all points.
Motion in a Straight Line Important Extra Questions Short Answer Type
Prove that the average velocity of a particle over an interval of time is either smaller than or equal to the average speed of the particle over the same interval.
Average velocity is defined as the ratio of the total displacement to the total time. Average speed is defined as the ratio of the total distance to the total time. Since displacement is less than or equal to the distance, therefore the average velocity is less than or equal to the average speed.
Two trains each of the length 109 m and 91 m are moving in opposite directions with velocities 34 km h-1 and 38 km h-1 respectively. At what time the two trains will completely cross each other?
Let l1, l2 be the lengths of the two trains.
v1, v2 be their velocities respectively.
∴ l1 = 109m, l2 = 91 m, v1 = 34kmh-1, v2 = 38kmh-1.
As the trains are moving in opposite directions so relative velocity of the trains is given by
v1 – (- v2) = v1 + v2
= 34 + 38 = 72 kmh-1
= 72 × 5/18 = 20 ms-1
otal distance to be covered by the two trains in crossing each other
= l1 + l2= 109 + 91 = 200 m
If t be the time taken in crossing, then t can be calculated using the relation
x = vt
t = 200/20 = 10s
Ambala is at a distance of 200 km from Delhi. Ram sets out from Ambala at a speed of 60 km h-1 and Sham set out at the same time from Delhi at a speed of 40 km h-1. When will they meet?
S = 200 km. Let VR and vs be the speeds of Ram and Sham respectively moving in opposite directions.
∴ vR = 60 kmh-1, vS = 40 kmh-1.
∴ Relative velocity of Ram w.r.t. Sham is
VRS = VR – (- VS)
= VR + VS
= 60 + 40 = 100 kmh-1
If t = time after which they will meet, then
t = time taken in covering 200 km distance with VRS
i.e. t = 200/vRS=200 km/100kmh−1 = 2h.
∴ Time after which they meet = 2h.
A car travelling at a speed of 60 km h-1 on a straight road is ahead of a scooter travelling at a speed of 40 km h-1. How would the relative velocity be altered if the scooter is ahead of the car?
vc = speed of car = 60 kmh-1
vs = speed of scooter = 40 kmh-1
vcs = relative velocity of car w.r.t. scooter
= vc – vs
= 60 – 40
= 20 kmh-1
Similarly vsc = relative velocity of scooter w.r.t. car
= vs – vc
= 40 – 60
= – 20 kmh--1
Thus we conclude that the magnitude of the relative velocity is the same in both cases but the direction of relative velocity is reversed if the scooter is ahead of the car.
Draw the position-time graphs for two objects initially occupying different positions but having zero relative velocity.
The positive T time graphs for two objects initially occupying different positions but having zero relative velocity are parallel to each other as shown in Fig.
A ball is thrown vertically upward with a velocity of 20 ms-1. It takes 4 seconds to return to its original position. Draw a velocity-time graph for the motion of the ball and answer the following questions:
At which point P, Q, R, the stone has :
(a) reached its maximum height.
(b) stopped moving?
Let P represent the initial position at the time when the ball is thrown vertically upward.
Q represents the highest point reached by the ball.
R represents the original position of the ball after 4 seconds.
Thus the velocity-time graph for the motion of the ball is as shown in Fig.
(a) We know that at the highest point, the velocity of the object is zero. So stone will reach its maximum height corresponding to point Q.
(b) The stone has stopped moving at point Q because at Q, v = 0.
“It is the velocity and not the acceleration which decides the direction of motion of a body.” Justify this statement with the help of a suitable example.
The direction of velocity is always in the direction of motion of the body whereas the direction of acceleration may or may not be in the direction of motion of the body. Thus we conclude that it is the velocity that decides the direction of motion of the body.
Example: When a ball is thrown vertically upwards, the direction of motion of the ball and velocity is the same i.e. vertically upwards. On the other hand, the acceleration due to gravity on the ball acts vertically downwards i.e. opposite to the direction of motion of the ball.
What are the important points about the uniform motion?
The following are some important points about the uniform motion:
- The velocity in uniform motion does not depend upon the time interval (t2 – 1,).
- The velocity in uniform motion is independent of the choice of origin.
- The average and the instantaneous velocities have the same value in uniform motion.
- No force acts on the object having uniform motion.
- Velocity is taken to be positive when the object moves toward the right of the origin and it is taken -ve if an object moves toward the left of the origin.
Is it possible that the velocity of an object be in a direction other than the direction of acceleration? When?
Yes, when a body moves in a circular path, then the direction of the velocity is along the tangent to the point on the circle and the acceleration is always towards its centre.
Is the rate of change of acceleration with the time important to describe the motion of a body? Why?
No, because it is observed that only velocity and acceleration are sufficient to understand and explain the motion of a body.
Explaining with an example, why does a person sitting in a train think that the other train is at rest when both are moving on parallel tracks with the same speed and in the same direction?
This is because the relative velocity of the train in which the person is sitting w.r.t. the other train is zero.
e.g. Let two trains A and B are moving along east with a velocity of 50 km/h i.e. vA = vB = 50 kmh1.
∴ relative velocity of A w.r.t. B is given by
VAB = vA – vB = 50 – 50 = 0.
Can a body be said to be at rest as well as in motion? Explain.
Yes, both rest and motion are relative terms. A body at rest w.r.t. one object may be in motion w.r.t. another object, e.g. a person sitting in a moving train is at rest w.r.t. other passengers in the train but at the same time, he is in motion w.r.t. the surroundings (trees or buildings) on the side of the track.