Question

A car came to rest when a brake was applied for $4s$ to get a retardation of $3m/{s^2}$. Calculate how far the car would have travelled after applying the brake.

Answer 1

Hint
We can find the distance travelled by the car after the brake was applied by using the equations of motion. By substituting the values of the final velocity and time we can find the initial velocity and then with the initial velocity we can find the distance travelled.
In this solution we will be using the following formula,
$\Rightarrow S = ut + \dfrac{1}{2}a{t^2}$
where $S$ is the distance travelled, $u$ is the initial velocity, $a$ is the acceleration and $t$ is the time.
and, $v = u + at$
where $v$ is the final velocity.

Complete step by step answer
In the given problem, first we need to find the initial velocity of the body at the beginning of the retardation. This can be calculated by the equations of motion given by,
$\Rightarrow v = u + at$
Here we substitute the final velocity of the body as, $v = 0m/s$, acceleration of the body is $\Rightarrow a = - 3m/{s^2}$, the negative sign is because the body is retarding, and the time is $t = 4s$. Therefore, we get,
$\Rightarrow 0 = u - \left( {3 \times 4} \right)$
Hence we get the initial velocity of the car as, $u = 12m/s$
Now using this value of the initial velocity, the time and the acceleration, we can find the distance travelled by the body from the equations of motion by,
$\Rightarrow S = ut + \dfrac{1}{2}a{t^2}$
On substituting the values, $u = 12m/s$, $a = - 3m/{s^2}$ and $t = 4s$, we get
$\Rightarrow S = \left( {12 \times 4} \right) + \left[ {\dfrac{1}{2} \times \left( { - 3} \right) \times {{\left( 4 \right)}^2}} \right]$
on doing the calculation in the brackets we get,
$\Rightarrow S = 48 - 24$
Therefore, the distance travelled is given as, $S = 24m$
So the distance that the car travels after the brakes are applied in time $4s$ is $24m$.

Note
Under uniform acceleration, equations of motion are also called the equations of constant acceleration. They are used to relate the displacement of a body with its velocity, acceleration and time.