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 find out how long after the trooper starts the chase he overtakes the speeding car, we can use the equations of motion. Let's break down the problem step by step:

Step 1: Determine the initial conditions for both the car and the trooper.
- The car's initial speed (u₁) = 33.4 m/s
- The trooper's initial speed (u₂) = 0 m/s (since the trooper starts from rest)
- The trooper's acceleration (a₂) = 3.28 m/s²

Step 2: Find the time it takes for the trooper to catch up to the car.
Let's assume the time taken by the trooper to catch up the car is 't'.
At this time t, the distance traveled by the car (s₁) would be the same as the distance traveled by the trooper (s₂).

Step 3: Calculate the distance traveled by both the car and the trooper.
- The distance traveled by the car (s₁) = u₁ * t
- The distance traveled by the trooper (s₂) = u₂ * t + 0.5 * a₂ * t² (using the equation of motion s = ut + 0.5at²)

Step 4: Equate the distances traveled by the car and the trooper.
Setting s₁ = s₂, we get:
u₁ * t = u₂ * t + 0.5 * a₂ * t²

Step 5: Solve the equation to find the value of 't'.
Rearranging the equation, we have:
u₁ * t - u₂ * t = 0.5 * a₂ * t²
(t * (u₁ - u₂)) = 0.5 * a₂ * t²
(t * (u₁ - u₂)) / (0.5 * a₂) = t

Step 6: Calculate 't'.
Substituting the given values, we have:
t = (33.4 m/s * 1 s) / (0.5 * 3.28 m/s²)
t = 33.4 m/s / 1.64 m/s²
t ≈ 20.36 s

Therefore, it will take approximately 20.36 seconds after the trooper starts the chase to overtake the speeding car.