Question

When a force F acts on a stationary body for the time t, the distance covered by the body will be proportional to

• A. t
• B. 1/t
• C. t²
• D. 1/t²

Answer 1

Answer: (C)

Step 1: Given that:

The force acting on the body = $F$

Initial velocity($u$) of the stationary body on which the force is applied= $0$

Time= $t$

Step 2: Determination of the distance covered by the body:

1. According to Newton's laws of motion, when a force is applied to a body, it produces an acceleration in the body.​
2. Acceleration changes the velocity of the body.
3. It may cause the body to move.
4. The distance covered by a body due to acceleration is given by the equation of motion.

According to the second equation of motion, $s=ut+\frac{1}{2}a{t}^2$ ,

Where, $a$ = Acceleration in the body

$u$ = Initial velocity of the body

$t$ = Time taken by the body

s= Distance covered by the body

Thus,

The distance covered by the body in given situation will be;

$s=0+\frac{1}{2}a{t}^2$

Where $a$ is the acceleration produced in the body due to the force $F$ on the body.

It is obvious, that

The distance covered by the body is

a) Directly proportional to the acceleration produced in the body, which is caused by the force on the body. That is $s\propto a$ , where, $a\propto F$

b) Directly proportional to the square of the time taken by the body.That is $s\propto t^2$

Thus,

Option C) $t^2$ is the correct option.