Question

Car A is traveling at a constant speed at a location where the speed limit is 100 km/h. The police officer 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 (a) until a speed of 160 km/h is achieved, and that speed is then maintained. Determine the distance required for the police officer to overtake car A. Neglect any nonrectilinear motion of P.

a) ( 160^2 - 100^2/2a )

b) ( 160^2 - 100^2/a )

c) ( 160^2 - 100^2/4a )

d) ( 160^2 - 100^2/8a )

Answer 1

The distance required for the police officer to overtake car A is (160^2 - 100^2)/(2a).

Step-by-step explanation:

To determine the distance required for the police officer to overtake car A, we need to first find the time it takes for the police car to reach a speed of 160 km/h. We can use the equation for displacement with initial velocity (vo) of 0 and constant acceleration (a) of (a): x = xo + vot + 1/2at². Plugging in the values, we get x = 0 + 0t + 1/2at². Since the car starts from rest, xo and vo are both 0. Rearranging the equation to solve for time (t), we get t = sqrt(2x/a). Here, x is the distance required for the police car to reach a speed of 160 km/h and a is the acceleration.

After finding the time it takes for the police car to reach 160 km/h, we can find the distance traveled by car A during that time. Since car A is traveling at a constant speed of 100 km/h, we can use the formula d = vt, where d is the distance traveled, v is the velocity, and t is the time. Plugging in the values, we get d = 100t.

To find the distance required for the police officer to overtake car A, we subtract the distance traveled by car A from the distance required for the police car to reach 160 km/h. So the distance required for the police officer to overtake car A is (160^2 - 100^2)/(2a).