a speedster traveling at a constant speed of 120 km/h passes a waiting police car which immediately starts from rest with a constant acceleration of 2.5 m/s^2.how long will it take the police car to catch the speedster?what is the distance that the speedster would have travel when caught by the police?
just see when the distances are equal:
120km/hr = 100/3 m/s, so
100/3 t = 2.5/2 t^2
t = 80/3
Now I expect you can handle the rest . . .
I DO APPREACIATE YOUR HELP,BUT AM STILL LITTLE CONFUSED
Helped
To find out how long it will take for the police car to catch the speedster and the distance the speedster would have traveled when caught by the police, we can use the equations of motion.
Let's start by finding the time it takes for the police car to catch up to the speedster:
Step 1: Convert the speed of the speedster from km/h to m/s.
- Speed of the speedster = 120 km/h
- Speed of the speedster in m/s = 120 km/h * (1 km/3600 s) * (1m/1 km)
= (120 * 1000)/(3600 * 1) m/s
≈ 33.33 m/s
Step 2: Use the equation for the position of an object with constant acceleration:
- s = ut + (1/2)at^2
where s = distance, u = initial velocity, a = acceleration, and t = time.
Let's assume that the initial position of the police car is at point A, and the speedster is at point B when t = 0.
Step 3: Use the same equation for both the speedster and the police car. We can set up two separate equations:
- For the speedster:
s1 = 33.33t
- For the police car:
s2 = 0 + (1/2) * 2.5 * t^2
Step 4: Find the time at which the police car catches up to the speedster.
- When the police car catches the speedster, the distances covered by both are equal. Therefore, s1 = s2.
- 33.33t = (1/2) * 2.5 * t^2
- Simplifying, we get:
66.66t = 1.25t^2
- Rearranging, we get:
1.25t^2 - 66.66t = 0
- Factoring out t, we get:
t(1.25t - 66.66) = 0
- Solving for t, we find two solutions:
t = 0 (which is the starting point) and t ≈ 53.33s
Since time cannot be negative, we discard the solution t = 0.
So, the police car will take approximately 53.33 seconds to catch the speedster.
Step 5: Calculate the distance the speedster would have traveled when caught by the police car.
- Using the equation s1 = 33.33t, we plug in t = 53.33s:
s1 = 33.33 * 53.33
s1 ≈ 1777.78m
Therefore, the speedster would have traveled approximately 1777.78 meters when caught by the police car.