Question

Find the initial velocity of the car which is stopped in $10{\text{seconds}}$ by applying brakes. The retardation due to brakes is $2.5m/{s^2}$.

Answer 1

The given question can be solved with the help of the formula that is derived from the acceleration point of view. Use the formula that involves acceleration, time, and velocities.

Formula used:
$\Rightarrow v = u + at$
Where,
$v$ is the final velocity
$u$ is the initial velocity
$a$ is the acceleration
$t$ is the time.

Complete step by step answer:
The given question can be solved with the help of the first equation of motion. The first equation of motion involves the acceleration, time, and initial and final velocities.
The first equation of motion deals with the finding of the final velocity that is obtained by adding the initial velocity and multiplying the acceleration and time. Mathematically it can be represented as,
$\Rightarrow v = u + at$
Where,
$v$ is the final velocity
$u$ is the initial velocity
$a$ is the acceleration
$t$ is the time.
Consider the values given in the question, the value for the final velocity is not given in the given question. Therefore, we can consider the $v$ as zero. The value of time is $10{\text{seconds}}$. The retardation value is $2.5m/{s^2}$.
The retardation is the opposite of the acceleration. And hence the $2.5m/{s^2}$ sign will be changed into negative.
Let us substitute the values in the equation. The initial velocity value needs to be found. The above equation can be written as,
$\Rightarrow u = - v + at$
$\Rightarrow u = 0 - \left( { - 2.5 \times 10s} \right)$
Use multiplication to solve the terms inside the bracket.
$\Rightarrow u = 0 - \left( { - 25} \right)$
When we multiply the negative signs, we get a plus sign.
$\Rightarrow u = 0 + 25$
Add to get the answer.
$\Rightarrow u = 25m/s$

Therefore, the value of the initial velocity is $u = 25m/s$.

Note: The first equation of motion can be mathematically derived by using the formula for the acceleration. Acceleration can be defined as the rate of change of velocity. That is,
$\Rightarrow a = \dfrac{v}{t}$
Velocities can be expressed as initial and final velocity.
$\Rightarrow a = \dfrac{{v - u}}{t}$
The first equation motion is used to find the value of the final velocity. Therefore, the above equation can be written as,
$\Rightarrow v = u + at$