Question

An object is covering distance in direct proportion to the square of time elapsed. What conclusion can be drawn about the motion of the object?
(1) The object is moving with zero acceleration
(2) The acceleration of the object is constant
(3) The object is moving with increasing acceleration
(4) The object is moving with decreasing acceleration.

Answer 1

Correct Answer is : Option 2:

The acceleration of the object is constant

Reason:

According to question,

Distance Travelled = d= kt²--------------1

where k is symbol of propritionality

t is time

Differentiating equation 1 w.r.t time we get:

speed=v=2kt---------2

again differentiating equation 2 with respect time we get

acceleration=2k a constant value

Hence The acceleration of the object is constant

Answer 2

distance covered by the object is directly proportional to square of time elapsed.
e.g., $S\propto t^2$
or, S = kt² , where k is proportionality constant.

differentiate with respect to time,
dS/dt = 2kt
we know , rate of change of distance is known as speed ,
so, speed , v = 2kt
hence speed of object is directly proportional to time elapsed.

again differentiate with respect to time,
dv/dt = 2k
we know, rate of change of speed is known as acceleration { magnitude}
hence, acceleration = 2k

here it is clear that acceleration of the object is constant.

hence, option (2) is correct.