Question

A car moving with a velocity of $10\, m / s$ can be stopped by the application of a constant force $F$ in a distance of $20\, m$. If the velocity of the car is $30\, m/s$ 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
$v^{2}-u^{2}=2 a s$
After applying the brakes car will come to rest $v =0$
$u ^{2} \propto s$
$\therefore \frac{ s _{1}}{ s _{2}}=\frac{ u _{1}^{2}}{ u _{2}^{2}} \Rightarrow s _{2}=\left(\frac{ u _{2}}{ u _{1}}\right)^{2} \times s _{1}$
$s_{2}=\left(\frac{30}{10}\right)^{2} \times 20=9 \times 20=180\, m$