Question

A speeder traveling at a constant speed of 99 km/h races past a billboard. a patrol car pursues from rest with constant acceleration of (9 km/h)/s until it reaches its maximum speed of 161 km/h, which it maintains until it catches up with the speeder. how long does it take the patrol car to catch the speeder if it starts moving just as the speeder passes? answer in units of s.

Answer 1

The patrol car takes 17.89 seconds to reach its maximum speed and 28.89 seconds to catch up with the speeder. Therefore, it takes a total of 46.78 seconds for the patrol car to catch the speeder.

Step-by-step explanation:

To find the time it takes for the patrol car to catch the speeder, we need to calculate the time it takes for the patrol car to reach its maximum speed and the time it takes for the patrol car to catch up with the speeder.

First, let's calculate the time it takes for the patrol car to reach its maximum speed:

Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time:

161 km/h = 0 km/h + (9 km/h)/s * tmax

tmax = 161 km/h / (9 km/h)/s = 17.89 s

Next, let's calculate the time it takes for the patrol car to catch up with the speeder:

Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time:

99 km/h + 161 km/h = 0 km/h + (9 km/h)/s * tcatch

tcatch = 260 km/h / (9 km/h)/s = 28.89 s

Therefore, the total time it takes for the patrol car to catch the speeder is the sum of the time it takes to reach its maximum speed and the time it takes to catch up with the speeder:

Total time = tmax + tcatch = 17.89 s + 28.89 s = 46.78 s