Question

The velocity of a body depends on time according to the equation v = 20 + 0.1${{t}^{2}}$. The body is undergoing
A. uniform acceleration
B. uniform retardation
C. non- uniform acceleration
D. zero acceleration

Answer 1

Hint: In this question, we are given the velocity and we have to find out in which acceleration body is going. We know the rate of change of velocity is acceleration. So first we differentiate the given equation and then with the help of relation of acceleration and time we find out in which acceleration the body is going and choose the option accordingly.

Formula used:
We use the formula of velocity:-
\[\text{velocity}=\dfrac{\text{change in displacement}}{\text{time taken}}\]

Complete step by step solution:
Velocity is the rate of change of displacement of a body.
\[\text{velocity}=\dfrac{\text{change in displacement}}{\text{time taken}} \\ \]
And the rate of change of velocity is called the acceleration of the body.
$a=\dfrac{{{v}_{2}}-{{v}_{1}}}{{{t}_{2}}-{{t}_{1}}} \\ $
That is $a=\dfrac{dv}{dt} \\ $
Given v = 20 + 0.1${{t}^{2}} \\ $
We know acceleration is differentiating velocity with time.
That is a = $\dfrac{dv}{dt} \\ $
Then a = $\dfrac{d(20+0.1{{t}^{2}})}{dt} \\ $
$\therefore a = 0.2 t$
From the above, it is clear that acceleration depends upon the time or we say that the speed of the particle changes by time. So, it is a non- uniform acceleration.

Thus, option C is the correct answer.

Note: If the body is under uniform acceleration, then there will be constant acceleration with changes in time. If the acceleration depends on time, then the acceleration increases with increase in time or it will decrease with the decrease in time.