A car traveling at a constant speed of 33.4 m/s passes a trooper hidden behind a billboard. One second later the trooper starts the car with a constant acceleration of 3.28 m/s2 How long after the trooper starts the chase does he overtake the speeding car

To determine how long after the trooper starts the chase the car will be overtaken, we can use the equation of motion for the trooper's car:

v = u + at

Where:
v = final velocity (unknown)
u = initial velocity of the trooper's car (0 m/s, as the trooper starts from rest)
a = acceleration of the trooper's car (3.28 m/s^2)
t = time taken (unknown)

Given that the car is traveling at a constant speed of 33.4 m/s, the trooper's car needs to catch up to this speed in order to overtake it. Let's consider the time it takes for the trooper's car to reach the same speed as the speeding car.

Using the equation of motion for the car:

v = u + at

Where:
v = final velocity of the car (33.4 m/s)
u = initial velocity of the car (unknown)
a = acceleration of the car (0 m/s^2, as the car is traveling at a constant speed)
t = time taken (1 second later)

Since u is unknown, we need to solve for it. Rearranging the equation, we have:

u = v - at

Substituting the given values:

u = 33.4 m/s - 0 m/s^2 * 1 s
u = 33.4 m/s

Now, we can substitute the value of u into the equation for the trooper's car:

v = u + at

33.4 m/s = 0 m/s + 3.28 m/s^2 * t

Rearranging the equation, we have:

t = (v - u) / a

t = (33.4 m/s - 0 m/s) / 3.28 m/s^2
t = 33.4 m/s / 3.28 m/s^2
t ≈ 10.18 seconds

Therefore, the trooper will overtake the speeding car approximately 10.18 seconds after starting the chase.