A car is traveling at 22 6 ms and the driver sees a traffic

A car is traveling at 22 6 m/s. and the driver sees a traffic light turn red After 0 218 s (the reaction time), the driver applies the brakes and the car decelerates at 9 6 m/s^2. What is the stopping distance of the car, as measured from the point where the driver first sees the red light?

Solution

Initial Velocity of car

V_o=22.6 m/s

Final Velocity of car is zero ,since it comes to rest

V=0

acceleration of the car ,is negative since it decelarates

a=-9.6 m/s²

time taken to stop

t=0.218 s

The Car travels a distance

X₁=V_ot =22.6*0.218 =4.9268 m

After applying brake at t=0.218 s

V=V_o²+2aX₂

0 =22.6²-2*9.6*X₂

X₂=22.6²/19.2 =26.602 m

Total distance travelled by the car

X=X₁+X₂ =31.5 m