contestada

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.

Respuesta :

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

Ver imagen akinsanyaayomide23
Hashirriaz830

Answer:

the motion is shown below

[tex]v_{A}[/tex]=130 km/h==> 36.1 m/s

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

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

[tex]S_{p}=\frac{v_{p}^2 }{2a} =164.3 m[/tex]

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

clearly [tex]S_{a}[/tex]>[tex]S_{p}[/tex] so police will have to move

now

S=([tex]S_{a}[/tex]-[tex]S_{p}[/tex])=102.9m

V=[tex]v_{A}[/tex]-[tex]v_{p}[/tex]=8.3 m/s

[tex]t_{2}[/tex]=[tex]\frac{S}{V}[/tex]=12.4 s

[tex]T_{total}[/tex]=t+[tex]t_{2}[/tex]

       =19.8 s

Otras preguntas