A car is traveling at a steady 81 km/h in a 50 km/h zone. A police motorcycle takes off at the instant the car passes it, accelerating at a steady 8.2 m/s2 .
How far is the motorcycle from the car when it reaches this speed?
car:
81 km /hr * (1 hr/3600 s) * (1000 m/km) = 22.5 m/s
travels for time T
so xcar= 22.5 T
motorcycle
v = 8.2 t= 22.5
t = 22.5/8.2 = 2.74 seconds accelerating = T car
x cycle = (1/2) a t^2 = (1/2)(8.2)(2.74)^2 = 30.9 meters
and
xcar = 22.5 * 2.74 = 61.7 meters
61.7 - 30.9 = 30.8 meters behind