Question

A constant retarding force of $50\;{\text{N}}$ is applied to a body of mass ${\text{10}}\;{\text{kg}}$ moving initially with a speed of ${\text{10}}\;{\text{m/s}}$. How long the body takes to comes to rest?
A. ${\text{2}}\;{\text{s}}$
B. ${\text{4}}\;{\text{s}}$
C. ${\text{6}}\;{\text{s}}$
D. ${\text{8}}\;{\text{s}}$

Answer 1

Formula for force is given by,
$F = ma$. Obtain the value of acceleration from the equation of force.
According to laws of motion,
$v = u + at$. Obtain the value of required time, $t$ from that equation.

Complete step by step solution:
Given,
The force is, $F = - 50\;{\text{N}}$, (the applied force is a retarding force, hence we use negative sign before the numerical value of the force)
Mass of the body is given by, $m = {\text{10}}\;{\text{kg}}$
Initial speed of the body is given by, $u = {\text{10}}\;{\text{m/s}}$
Here, final speed of the body is, $v = 0\;{\text{m/s}}$
Now, we need to find the value of time, $t$.

We know that, the formula for force is deduced by Newton’s law, and is given by
$F = ma$, …… (i)
Where $F$ is force,
$m$ is mass of a body, and
$a$ is acceleration of the body.

In order to find the acceleration we rearrange the equation (i) as,
$a = \dfrac{F}{m}$ …… (ii)
Now substitute the value of $F = - 50\;{\text{N}}$ and $m = {\text{10}}\;{\text{kg}}$ in equation (ii).
Therefore,

a = \dfrac{{ - 50\;{\text{N}}}}{{10\;{\text{kg}}}} \\\ = - 5\;{\text{m/}}{{\text{s}}^{\text{2}}} \\\ \end{gathered} $$ Now, in order to find the required time we use the formula of motion, and is given by, $$v = u + at$$ Rearrange the above equation to find the value of $$t$$. $$t = \dfrac{{v - u}}{a}$$ …… (iii) Now, substitute the values of $$u = {\text{10}}\;{\text{m/s}}$$, $$v = 0\;{\text{m/s}}$$, and $$a = - 5\;{\text{m/}}{{\text{s}}^{\text{2}}}$$ in equation (iii) Therefore, $$\begin{gathered} t = \dfrac{{0\;{\text{m/s}} - 1{\text{0}}\;{\text{m/s}}}}{{ - 5\;{\text{m/}}{{\text{s}}^{\text{2}}}}} \\\ = \dfrac{{10}}{5}\;{\text{s}} \\\ = {\text{2}}\;{\text{s}} \\\ \end{gathered} $$ **Hence, the required time is $$2\;{\text{s}}$$.** **Note:** In this problem we are asked to calculate the value of time taken. For this, use the formula $$v = u + at$$ instead of $$S = ut + \dfrac{1}{2}a{t^2}$$ or $${v^2} - {u^2} = 2aS$$. But we need the value of $$a$$ to solve it. Now in order to find the value of $$a$$, use the formula $$F = ma$$. Subtract $$10\;{\text{m/s}}$$ from $$0\;{\text{m/s}}$$ to get the correct answer or else the time will come as negative.