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 it takes for the trooper to overtake the speeding car, we need to find the time it takes for the trooper to match the speed of the car.
Let's break down the problem using the following variables:
- Car's initial speed (u1) = 33.4 m/s
- Trooper's initial speed (u2) = 0 m/s (since the trooper starts from rest)
- Trooper's acceleration (a) = 3.28 m/s^2
- Time taken by the trooper to overtake the car (t)
We can use the formula of motion to find the time taken:
v = u + at
For the trooper:
trooper_speed = u2 + at
For the car:
car_speed = u1
We know that when the trooper overtakes the car, their speeds become equal. Therefore:
trooper_speed = car_speed
Substituting the values into the equation, we get:
u2 + at = u1
Since u2 = 0, the equation becomes:
at = u1
Therefore:
t = u1 / a
Plugging in the values, we find:
t = 33.4 m/s / 3.28 m/s^2
Calculating this expression:
t ≈ 10.18 seconds
So, the trooper will overtake the speeding car approximately 10.18 seconds after starting the chase.