Question

A body of mass 2 kg is at rest. What should be the magnitude of force which will make the body move with a speed of $30m{{s}^{-1}}$ at the end of 1s? 

Answer 1

Hint: According to Newton’s second law of motion, the magnitude of the applied force on a body is equal to the product of its mass and acceleration. Acceleration of a body is equal to the change in velocity of the body in one unit of time.

Formula used:
$F=ma$
Here, $m$ is the mass of the body and $a$ is the acceleration of the body.

Complete step by step answer:

Let us first understand what happens when a force of some magnitude is applied on a body. 

When an unbalanced force is applied on a body it changes its state of uniform motion. This means that if the body is at rest, the applied force will make the body move and if the body is moving at constant velocity, the applied force will change its velocity.

Therefore, when an unbalanced force is applied on a body, we say that the body accelerates.

Acceleration is defined as the rate of change in velocity of the body with respect to time. Acceleration of a body is equal to the change in velocity of the body in one unit of time. Therefore, if velocity of a body changes by a value ‘v’ in one unit of time then its acceleration is $a=v$

It is said that the body is at rest and moves with a speed of $30m{{s}^{-1}}$ at the end of 1s.

Therefore, the acceleration of the body is $a=30m{{s}^{-2}}$.From Newton’s second law of motion, we get that the applied force (F) is given as $F=ma$    … (i).

Here, m is the mass of the body.

It is given that $m=2kg$.

Substitute the value of ‘a’ and m in (i).

$\therefore F=(2)(30)=60m{{s}^{-2}}$

Therefore, the magnitude of force that will make the body move with a speed of $30m{{s}^{-1}}$ at the end of 1s is $60m{{s}^{-2}}$.

Note: Note that force is a vector quantity. Therefore, every force as a direction. Therefore, when more than one force acts on a body, a resultant vector of all the forces will be the effective force acting on the body. It may sometimes happen that the resultant of the forces may be zero, which means that the effective force on the body is zero. Hence, the acceleration of the body is zero. Then the  effective force is called balanced force. Therefore, we can conclude that to accelerate a body, an unbalanced force must be applied on it.