Question

A constant retarding force of $15\,N$ is acting on a body of mass $20\,kg$ moving with the initial velocity of $50\,m/s$. How long does the body take to stop?

Answer 1

Hint:In question we need to find out the acceleration of the object. This we can find out using the laws of motion. It states, the force applied on the body is the product of the mass and the acceleration of the body due to force. We will then try to find out time using the equations of motion.

Formula used:
$ a = \dfrac{{v - u}}{t} \\
F = ma \\ $
Here, $v$: final velocity, $u$: initial velocity, $t$: time and $a$: acceleration.

Complete step by step answer:
As given in the question we have,
Mass of the body(m) = $20\,kg$
Force acting on the body (F) = $15\,N$
Initial velocity of the body is (u) = $50\,m/s$
Final velocity as the object stops (comes to rest) is (v) = $0\,m/s$.

Using Newton’s second law of motion we can have, the force applied on or by a body is a product of mass and acceleration.
$F = ma$
Substituting the values we have in the equation
$ - 15 = 20 \times a \\
\Rightarrow a = \dfrac{{ - 15}}{{20}}
\Rightarrow a = - 0.75\,m{s^{ - 2}} \\ $
As we get the acceleration we can find out the time taken by the body to come to rest.
$ a = \dfrac{{v - u}}{t} \\
\Rightarrow - 0.75 = \dfrac{{0 - 50}}{t} \\ $
After cross multiplying and getting t on the left side
$t = \dfrac{{ - 50}}{{ - 0.75}} \\
\therefore t = 66.67\,s \\ $
So the body will take 66.67 seconds to come to rest.

Note: It is always good to remember when to use and when not to use Newton's laws of motion. Newton’s laws are applied if and only if the acceleration is constant. If it is not the case then the problem will be solved using the derivatives and functions and not the laws of motion. But in any case it is always best to remember Energy always remains constant.