Question

The reaction time for a car driver is 0.9 s. If the car travelling initially with 36 km/h is stopped by the driver after observing a signal by the deceleration of $5m/s^2,$ the total distance travelled by the car before coming to rest is:

• A. 19 m
• B. 9 m
• C. 10 m
• D. 28 m

Answer 1

Answer: (A)

Before deceleration the car has covered the distance $s_1=ut$ Given: u= 36 km/h $u=\frac{36\times 5}{18}=10m/s$ $t=0.9s$ $s_1=10\times 0.9=9m$ Again the time taken in travelling by the car after deceleration $v=u+gt$ $\left(\begin{array}{rl}& \because v=0\\ & a=-5m/s^2\end{array}\right)$ $0=10-5t_1$ $t_1=\frac{10}{5}=2s$ Now, the distance travelled by the car after deceleration is given by $s_2=u{t}_1+\frac{1}{2}a{t}^2$ $=10\times 2-\frac{1}{2}\times 5\times {(2)}^2$ $20-10=10m$ Hence, total distance travelled by car is given by = 9m + 10 m = 19m