MCQs Motion in one dimension

## Kinematics

Mechanics is the branch of physics which deals with the causes and effects of motion. Kinematics part of mechanics deals with the description of motion without reference to the forces which either cause its motion or are generated as a result of its motion. It is a very dif cult task to discuss the motion of a material body, as a material body consists of a large number of smaller constituents (atoms or molecules, we can say), which itself is in the state of motion. To simplify our discussion of motion of objects, we start with objects, whose position can be described by locating one point i.e., the size of the object is considerably very small as compared to the distance for which its motion is considered and its internal motion and rotational motion are of no interest to us. Such an object we call as a particle. The motion of particle will be discussed in terms of velocity, displacement, acceleration etc. Note: There is no limit on the size of the object for it to be treated as a particle, it totally depends on the situation whether an object can be treated as a particle or not. Even earth can be treated as a particle when we are interested in its nearly circular motion around the sun, while it can’t be treated as a particle when we are interested in its rotational motion about its own axis.

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1. A particle travels along a curved path between two points P
and Q as shown:

The displacement of the particle does not depend upon

(a) the location of P and Q
(b) the choice of origin
(c) the direction of Q from P
(d) the length of the line joining P and Q.

2. A particle is moving along x-axis whose position is varying with time according to the relation x = 3t +  t3 where x is in metres and t is in seconds. The displacement of particle for t
= 1 s to t= 3 s is

(a) 16 m                             (b) 26 m
(c) 20 m                            (d) 22 m

3. For a particle moving along a straight line, mark out the correct statement(s).
(a) Average speed is always equal to the magnitude of average
velocity measured for a particular time interval.
(b)  The particle is always speeding up.
(c) Distance travelled by particle is always equal to the magnitude of displacement.
(d) Instantaneous speed is always equal to the magnitude of the instantaneous velocity.

4. A particle is moving along a straight line with constant speed, then
(a) velocity of particle is constant
(b) acceleration of particle is zero
(c) acceleration of particle is non-zero
(d) None of the above

5. A particle is moving along a curved path with constant speed,
then
(a) the velocity of the particle is constant
(b) acceleration of the particle is zero
(c) acceleration of the particle is non-zero
(d) None of the above

6. During the first 18 min of a 60 min trip, a car has an average speed of 11 m/s. What should be the average speed for remaining 42 min so that car is having an average speed of 21 m/s for the entire trip?

(a) 25.3 m/s                                 (b) 10 m/s
(c) 31 m/s                                     (d) 16.4 m/s

7. Which one of the following situations is not possible?
(a) A particle having zero velocity and non-zero acceleration
(b) A particle having velocity in +ve X direction and acceleration along – ve X-direction.

(c) A particle having velocity in +ve X direction and acceleration along -ve Z-direction.
(d) a particle having a constant speed and constant acceleration.

8. A car starts from rest and accelerates at a constant rate in a straight line. In the first second the car covers a distance of 2 m, the velocity of the car at the end of second will be
(a) 4.0 m/s                                  (b) 8.0 m/s
(c) 16 m/s                                   (d) None of these.

9. Ball A is dropped from rest from a window. At the same instant, ball B is thrown downwards and ball C is thrown upwards from the same window. Which statement concerning the ball is necessarily true if air resistance is neglected?
(a) All three balls strike the ground at same time.
(b) All three balls strike the ground with the same velocity.
(c) All three balls have the same velocity at any instant.
(d) All three balls have same acceleration at any instant.
10. A particle is thrown vertically upwards from the surface of the earth. The particle rises to some maximum height and falls back towards the surface of the earth. Which one of the following statements concerning this situation is true? (Neglect air resistance).
(a) As the particle rises, its acceleration vector points upward.
(b) The particle is freely falling body for the duration of its flight.
(c) The acceleration and velocity of a particle are zero at the topmost point.
(d) The velocity and acceleration of particle are always pointing in the same direction.