question_answer

Reaction time of a driver is the time interval between the moment the driver sights an obstacle and the moment he applies the brakes. During this time the car travels with a constant speed at which he is driving and gets nearer to the obstacle. A driver has a reaction time of 0.5 s and is travelling at 72 kmph on a straight road. What should be the minimum deceleration produced by the brakes of his car if he should avoid hitting an obstacle 50 m away from the car at the moment he sees it?

Answer:

\[{{t}_{reaction}}=0.5s\,\,u=72\,kmph\] \[=72\times \frac{5}{18}=20m/s\] \[{{S}^{1}}=ut=0.5\times 20=10m\] Now distance left \[=50-10=40m,\,\,v=0,\,\,a=?\] using \[{{v}^{2}}-{{u}^{2}}=2as\] \[\Rightarrow {{0}^{2}}-{{(20)}^{2}}=2\times a\times 40\] \[\Rightarrow -400=80a\Rightarrow a=-5m/{{s}^{2}}\] \[\therefore \]The minimum deceleration produced by the brakes of the car is\[5m/{{s}^{2}}.\]