Question

A car moving along a straight highway with speed of $126km/hr$ is brought to a stop within a distance of $200m$. What is the retardation of the car and how long does it take for the car to stop?

Answer 1

Step 1: Given

Speed of the car, $u=126km/hr=35m/s$

Final speed of the car, $v=0$

Distance, $s=200m$

Step 2: Determine the acceleration $a$

Using the third equation of motion,

$$\begin{gathered} v^2=u^2+2as \\ {0}^2={35}^2+2\left(a\right)\left(200\right) \\ a=-\frac{{35}^2}{400} \\ =-3.065m/s^2 \end{gathered}$$

Negative acceleration suggests retardation.

Step 3: Determine the time taken

Using the first equation of motion,

$$\begin{gathered} v=u+at \\ 0=35+(-3.065)t \\ t=11.4s \end{gathered}$$

Therefore, The retardation of the car is $-3.065m/s^2$ and it takes the car $11.4s$ to stop.