Question

The following is the distance time table of an object in motion:

Time in seconds	Distance in metres
0	0
1	1
2	8
3	27
4	64
5	125
6	216
7	343

(A) What conclusions can you draw about the acceleration? Is it constant, increasing, decreasing or zero?
(B) What do you infer about the forces acting on the object?

Answer 1

Hint : To solve this question we have to know about velocity. We know that, The meaning of velocity of an object can be defined as the rate of change of the object’s position with respect to a frame of reference and time. It might sound complicated but velocity is basically speeding in a specific direction. It is a vector quantity, which means we need both magnitude (speed) and direction to define velocity. The SI unit of it is meter per second. If there is a change in magnitude or the direction in the velocity of a body the body is said to be accelerating.

Complete Step By Step Answer:
(a) There is an unequal change of distance in an equal interval of time. Thus, the given object is having a non - uniform motion. Since the velocity of the object increases with time, the acceleration is increasing.
(b) According to Newton's second law of motion, the force acting on an object is directly proportional to the acceleration produced in the object. In the given case, the increasing acceleration of the given object indicates that the force acting on the object is also increasing.

Note :
We also know that, Acceleration is defined as The rate of change of velocity with respect to time. Acceleration is a vector quantity as it has both magnitude and direction. It is also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time.