Question

A car moving with a velocity of $10m/s$ can be stopped by the application of a constant force $F$ in a distance of $20m$. If the velocity of the car is $30m/s$ it can be stopped by this force in:

• A. 100 m
• B. 120 m
• C. 180 m
• D. 160 m

Answer 1

Answer: (C)

According to the $3^{\text{rd }}$ equation of motion
$v^2-u^2=2as$
After applying the brakes car will come to rest $v=0$
$u^2\propto s$
$\therefore \frac{s_1}{s_2}=\frac{u_1^2}{u_2^2}\Rightarrow s_2={\left(\frac{u_2}{u_1}\right)}^2\times s_1$
$s_2={\left(\frac{30}{10}\right)}^2\times 20=9\times 20=180m$