question_answer

A driver takes 0.20s to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of 54km/h and the brakes cause a deceleration of \[\text{6}.0\text{m}/{{\text{s}}^{\text{2}}}\], Find the distance travelled by the car after he sees the need to put the brakes on.

Answer:

Reaction time, \[t=0.20s\] initial speed of the car, u = 54 km/hr \[=54\times \frac{5}{18}=15m/s\] deceleration, \[a=-6.0m{{s}^{-2}}.\] distance travelled during the reaction time, \[{{S}_{1}}=u\times {{t}_{1}}=15\times 0.2=3m\] After applying the breaks, the car travelled the distance, \[{{S}_{2}}=\frac{{{v}^{2}}-{{u}^{2}}}{2a}=\frac{0-{{(15)}^{2}}}{-2\times 6}=\frac{225}{12}=18.75m\] total distance travelled by the can after the sees the need to put the brakes on \[S={{S}_{1}}+{{S}_{2}}=3+18.75=21.75m\approx 22m\]