Question

The brakes applied to a car produce an acceleration $6\mathrm{m}{\mathrm{s}}^{-2}$ in opposite direction to the motion If the car takes $2\mathrm{s}$ to stop after the application of brakes calculate the distance it travels during this time

Answer 1

Step 1: Given Data

1. After applying the brakes the acceleration produced in the car is$6m/s^2$ which means the negative acceleration is$6m/s^2$.
2. At last, the car stops which means the final velocity$\left(v\right)$ is zero.
3. The car moved for a time$2s$.

Step 2: Calculating the initial velocity of the car

applying the first equation of motion we get

$v=u+at$

$\Rightarrow 0=u+\left(-6\right)\times 2$

$\Rightarrow u-12=0$

$\Rightarrow u=12m/s$

Step 3: Calculating the distance covered by the body

applying the third equation of motion we get

$v^2-u^2=2as$

$\Rightarrow 0-{12}^2=2\times \left(-6\right)\times s$

$\Rightarrow -144=-12s$

$\Rightarrow s=\frac{144}{12}=12m$

Hence, the distance covered by the car is$12m$.