Question

Here is my question :-
Q. A force F acts on a stationary body for the time t. The distance covered by the body 'S' will be proportional to :
(A) t
(B) 1/t
(C) t^2
(D) 1/(t)^2
Explain your answer .
And correct answer is (C). Why ?

Answer 1

We are said that a Force F acts on a stationary body for time t.

Since a constant Force is acting, the body has constant acceleration for time t. In other words, the motion of body is uniformly accelerated for time t.

If the mass of the body is m, then we have:

$\displaystyle F=ma \\ \\ \\ \implies a=\frac{F}{m}$

Thus, an acceleration a acts on the body for time t. Now we can find the distance s covered by the body in this time.

Also, the body was initially stationary. So initial velocity is zero.

We use the following equation of motion:

$\displaystyle s=ut+\frac{1}{2}at^2 \\ \\ \\ \implies s=(0)t+\frac{1}{2}\times \frac{F}{m} \times t^2 \\ \\ \\ \implies s= \frac{F}{2m} \, t^2 \\ \\ \\ \implies \boxed{\bold{s \propto t^2}}$

Thus, The distance travelled by the body in time t is proportional to $\bold{t^2}$

So, The Answer is Option (C) $\bold{t^2}$

Answer 2

Answer:

We are said that a Force F acts on a stationary body for time t.

Since a constant Force is acting, the body has constant acceleration for time t. In other words, the motion of body is uniformly accelerated for time t.

If the mass of the body is m, then we have:

\begin{gathered}\displaystyle F=ma \\ \\ \\ \implies a=\frac{F}{m}\end{gathered}F=ma⟹a=mF

Thus, an acceleration a acts on the body for time t. Now we can find the distance s covered by the body in this time.

Also, the body was initially stationary. So initial velocity is zero.

We use the following equation of motion:

\begin{gathered}\displaystyle s=ut+\frac{1}{2}at^2 \\ \\ \\ \implies s=(0)t+\frac{1}{2}\times \frac{F}{m} \times t^2 \\ \\ \\ \implies s= \frac{F}{2m} \, t^2 \\ \\ \\ \implies \boxed{\bold{s \propto t^2}}\end{gathered}s=ut+21at2⟹s=(0)t+21×mF×t2⟹s=2mFt2⟹s∝t2

Thus, The distance travelled by the body in time t is proportional to \bold{t^2}t2

So, The Answer is Option (C) \bold{t^2}t2