Question

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

• A. $3.06m/s^2$ and $11.4s$
• B. $2.06m/s^2$ and $11.4s$
• C. $3.06m/s^2$ and $10.4s$
• D. $3.06m/s^2$ and $4.1s$

Answer 1

The correct option is A $3.06m/s^2$ and $11.4s$

Given,

Velocity of car $v=126km/h=35m/s$

Displacement $s=200m$

Final velocity $v=0m/s$

Apply second kinematic equation to calculate retardation $a$

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

$\Rightarrow a=\frac{v^2-u^2}{2s}=\frac{0-{35}^2}{2\times 200}=-3.0625m/s^2$

Apply first kinematic equation to calculate time $t$

$v=u+at$

$\Rightarrow t=\frac{v-u}{a}=\frac{0-35}{3.0625}=11.43\sec$

Hence, retardation is $3.06m/s^2$ and time take to stop is $11.4\sec$