Question

A car of mass $1000kg$ is moving with a certain speed when a constant braking force $1000N$ acts on it for $5s$ and the speed of the car reduces to half its original speed. Find the further time required to stop the car if the same constant force acts.

Answer 1

Step 1: Given data

$$\begin{gathered} Force\left(F\right)=1000N \\ Massofthecar\left(m\right)=1000kg \\ Initialtime\left(t\right)=5s \end{gathered}$$

Step 2: Calculating initial velocity

We know that, $Force\left(F\right)=ma$

Hence, $a=\frac{F}{m}=\frac{1000}{1000}=1m{s}^{-2}$

Here the acceleration is equal to retardation. Therefore $a=-1m{s}^{-2}$.

According to the first equation of motion, $v=u+at$

Substitute $v=\frac{u}{2}$ (given that the speed of the car reduces to half its original speed).

$$\begin{gathered} \frac{u}{2}=u+(-1)\times 5 \\ -\frac{u}{2}=-5\Rightarrow u=10m{s}^{-1} \end{gathered}$$

Here the $Finalvelocity\left(v\right)=0$

Speed of the car when braking $u=\frac{u}{2}=5m{s}^{-1}$.

Step 3: Calculating the time required

$$\begin{gathered} v=u+at \\ 0=5+(-1)\times t \\ -5=-t \\ t=5s \end{gathered}$$

Thus, the further time required to stop the car is $5s$.