An unmarked police car traveling a constant 95 km/h is passed by a speeder traveling 120 km/h.
Precisely 1.00 sec. after the speeder passes, the police officer steps on the accelerator; if the police car's acceleration is 1.90 m/s^2 , how much time passes before the police car overtakes the speeder after the speeder passes (assumed moving at constant speed)?
6.1 seconds
6.1
I did not understand
To find out how much time passes before the police car overtakes the speeder, we need to determine the distance covered by both vehicles in the time it takes for the police car to catch up. Here's how we can calculate it:
1. Convert the speeds to meters per second (m/s) to keep the units consistent. The speed of the police car is 95 km/h, which is 26.389 m/s (since 1 km/h = 1000 m/3600 s) and the speed of the speeder is 120 km/h, which is 33.333 m/s.
2. Calculate the distance covered by the speeder in the 1.00 second after passing the police car. The formula for distance covered with constant speed is: distance = speed * time. In this case, we have distance = 33.333 m/s * 1.00 s = 33.333 meters.
3. Now, let's find out how long it will take for the police car to catch up to the speeder. We'll use the following kinematic equation: final velocity^2 = initial velocity^2 + 2 * acceleration * distance.
- The initial velocity is 26.389 m/s because that's the speed of the police car.
- The final velocity is 33.333 m/s because that's the speed of the speeder.
- The acceleration is 1.90 m/s^2 because that's the police car's acceleration.
- The distance is the same as the one we calculated in step 2, which is 33.333 meters.
Plugging those values into the equation, we get: (33.333 m/s)^2 = (26.389 m/s)^2 + 2 * (1.90 m/s^2) * distance.
4. Rearrange the equation to solve for the distance: distance = [(33.333 m/s)^2 - (26.389 m/s)^2] / (2 * 1.90 m/s^2).
Evaluating this equation, we find: distance = 85.818 meters.
5. Finally, we can calculate the time it takes for the police car to catch up to the speeder using the formula time = distance / speed. In this case, time = 85.818 meters / 26.389 m/s = 3.257 seconds.
Therefore, it takes approximately 3.257 seconds for the police car to overtake the speeder after the speeder passes.
Write two equations for distance travelled vs time after the speeder passes. One equation for each car.
Set the distances equal and solve for the time t.
V1 = 120 km/h = 33.33 m/s is the speeder's speed
V2 = 26.39 m/s + 1.90 (t-1)
is the policeman's speed,for t>1 s. For 0<t<1, it is 26.39 m/s
X1 (the speeder) = 33.33*t
X2 (the cop) = 26.39*t + 0.95(t-1)^2
Use X1 = X2 to solve for t