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 $ 5\text{ }m/{{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}=10\,m/s $ $ t=0.9\,s $ $ {{s}_{1}}=10\times 0.9=9\,m $ Again the time taken in travelling by the car after deceleration $ v=u+gt $ $ \left( \begin{align} & \because \,v=0 \\ & a=-5\,m/{{s}^{2}} \\ \end{align} \right) $ $ 0=10-5{{t}_{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=10\,m $ Hence, total distance travelled by car is given by = 9m + 10 m = 19m