Question

A body starts to slide over a horizontal surface with an initial velocity of $0.5\,m/s$. Due to friction its velocity decreases at the rate of $0.05\,m/s$. How much time will it take for the body to stop?

Answer 1

We are asked to calculate the time taken by the body to stop. This means that we take the final velocity as zero. We are given the value of initial velocity and rate of decrease of velocity, which is negative acceleration or deceleration. We have all the required values. We can simply apply the value on the equation of motion and end up with the required solution. The equation of motion as well as the formula to find the acceleration can be used here as both ultimately give us the same formula to find time.

Formulas used:
The final velocity of a body is given by the equation of motion as,
$v = u + at$
Where $a$ is the acceleration of the body, $u$ is the initial velocity of the body and $t$ is the time taken by the body to come to rest.

Complete step by step answer:
Let us start by writing down the values given to us,
The initial velocity with which the body is moving is $u = 0.5\,m/s$.
The negative acceleration of the body is, $a = - 0.05\,m/{s^2}$.
Now we apply this value to the equation of motion, $v = u + at$.
We get,

\Rightarrow t= \dfrac{{0 - 0.5}}{{0.05}} \\\ \therefore t= 10\,s$$ **Therefore, we get the time for the body to return to rest or to stop as, $$10\,s$$.** **Note:** We take the value of acceleration to be negative because it is given as the rate at which the velocity decreases. When the velocity of a body decreases, it causes the body to have a negative acceleration, also called deceleration. The definition of deceleration can be easily said as the rate at which the velocity decreases.