Question

A bus running at a speed of $18km/h$ is stopped in $2.5{\text{ seconds}}$ by applying brakes. Calculate the retardation produced.

Answer 1

Hint: Since we have to find the retardation, and as we know retardation is the negative of acceleration. So for finding this we will use the formula of final velocity and is given by, $v = u + at$ . And from this, we can easily get the acceleration and then the opposite of it will be the retardation.

Formula used
The final velocity is given by,
$v = u + at$
Here, $v$ is the final velocity
$u$ , is the initial velocity
$a$ , is the acceleration
$t$ , is the time.

Complete step by step answer:
So here in this question we have the initial velocity, $u = 18km/h$
First, we will convert this into meter per second, so for this
$ \Rightarrow u = 18 \times \dfrac{{1000}}{{3600}}$
And on solving it we get
$ \Rightarrow u = 5m/s$
The final velocity is given by, $v = 0m/s$ and the time will be equal to, $t = 2.5\sec $
Therefore, to find the acceleration we will use the formula given by
$ \Rightarrow v = u + at$
And on solving it for the acceleration, we will get the above equation as
$ \Rightarrow a = \dfrac{{v - u}}{t}$
And on substituting the values, we will get the equation as
$ \Rightarrow - \dfrac{{0.5}}{{2.5}}m/{s^2}$
And on solving the above expression, we will get the equation as
$ \Rightarrow - 2m/{s^2}$
And as we know that the retardation is the negative of acceleration, so from this we will get the retardation value as $2m/{s^2}$ .
Hence, the retardation is $2m/{s^2}$ .

Note:
The relation $v = u + at$ is the equation of motion which will describe the relationship between the velocity and time. And also in most of the cases, the value of the acceleration is constant or either it will give. While solving this type of question, we always check the unit once, so that we don’t come up with the unit conversion problem.