Question

A constant retarding force of $50\,{\text{N}}$ is applied to a body of mass $20\,{\text{kg}}$ moving initially with a speed of $15\,{\text{m}}{{\text{s}}^{ - 1}}$ . How long does the body take to stop?
A. $6\,{\text{s}}$
B. $4\,{\text{s}}$
C. $7\,{\text{s}}$
D. $2\,{\text{s}}$

Answer 1

First of all, we will find the acceleration by using Newton's law of motion, then use this acceleration to find the final velocity. Substitute the values and manipulate accordingly.

Complete step by step answer:
In the given question, the constant retarding force is $50\,{\text{N}}$ .
The mass of the body is given as $20\,{\text{kg}}$ .
The initial speed of the body is $15\,{\text{m}}{{\text{s}}^{ - 1}}$ .
We are asked to find the time taken by the body to come to rest.
It means that the final velocity of the body must be zero in the end.

For this we will apply the equations of laws of motion and Newton’s second law of motion:
In the first case we have to calculate the acceleration first, then we will go for manipulating the other quantities.

We have an equation from Newton’s laws of motion, which gives:
$F = ma$ …… (1)
Where,
$F$ indicates the force acting on the body.
$m$ indicates the mass of the body.
$a$ indicates the acceleration on the body.

Now, substituting the required values in the equation (1), we get:
$F = ma \implies - 50 = 20 \times a \\\ \implies a = - \dfrac{{50}}{{20}} \\\ \implies a = - \dfrac{5}{2}\,{\text{m}}{{\text{s}}^{ - 2}} \\\$
The acceleration is negative in nature, which means the acceleration is retarding in nature.
The acceleration of the body is found to be $- \dfrac{5}{2}\,{\text{m}}{{\text{s}}^{ - 2}}$ .

Now, we go on to find the time taken by the body to come to rest i.e. final velocity must be zero.
We apply an equation of laws of motion, which is as follows:
$v = u + at$ …… (2)
Where,
$v$ indicates the final velocity.
$u$ indicates the initial velocity.
$a$ indicates the acceleration.
$t$ indicates the time taken by the body.
Now, we substitute the required values in equation (2), we get:
v = u + at \\\ \implies 0 = 15 + \left( { - \dfrac{5}{2}} \right)t \\\ \implies \dfrac{{5t}}{2} = 15 \\\ \implies 5t = 2 \times 15 \\\

We will simplify the above expression to find the time:
5t = 2 \times 15 \\\ \implies t = \dfrac{{2 \times 15}}{5} \\\ \implies t = 2 \times 3 \\\ \therefore t = 6\,{\text{s}} \\\
Hence, the time required by the body is $6\,{\text{s}}$

So, the correct answer is “Option A”.

Note:
This can be solved by having some knowledge on the laws of motion. There is an alternative solution for this to, if you take force as positive then the acceleration will come out to be positive too. If the acceleration comes out to be positive, then use the equation $v = u - at$ , as the force is retarding in nature.