Question

Car A is traveling at a constant speed vA = 130 km / h at a location where the speed limit is 100 km / h. The police offi cer in car P observes this speed via radar. At the moment when A passes P, the police car begins to accelerate at the constant rate of 6 m/s2 until a speed of 160 km / h is achieved, and that speed is then maintained. Determine the distance required for the police offi cer to overtake car A. Neglect any nonrectilinear motion of P.

Answer 1

Answer:

Distance = 713.303m

Explanation:

To determine the distance required for the police officer to overtake car A, we simply calculate the time t for which the police car and the speeding car have traveled equal distances from point P

Answer 2

Answer:

the motion is shown below

$v_{A}$=130 km/h==> 36.1 m/s

$v_{p}$=0, a=6 m/s^2 (till $v_{p}$=160 km/h)

so time taken to reach $v_{p}$=160 km/h==> 44.4 m/s t=7.4 sec

$S_{p}=\frac{v_{p}^2 }{2a} =164.3 m$

in this time the car A travelled distance ($S_{a}$) is given by $S_{a}$=$v_{p}$*t=267.2 m

clearly $S_{a}$>$S_{p}$ so police will have to move

now

S=($S_{a}$-$S_{p}$)=102.9m

V=$v_{A}$-$v_{p}$=8.3 m/s

$t_{2}$=$\frac{S}{V}$=12.4 s

$T_{total}$=t+$t_{2}$

       =19.8 s