Answer:
The police car needs 19.6 s to catch the speeder.
Explanation:
Assuming a straight motion, these are the kinematic equations that we could use to solve the problem:
For the speeder that moves at a constant speed, the equation to determine its position after a time "t" is:
X = X0 + v*t
For the police car, which has a uniform acceleration, the position after a time "t" is:
X = X0 + v0*t + 1/2*a*t²
where:
X = position
X0 = initial position
v = velocity
v0 = initial velocity
t = time
a = acceleration
We have to find how much time needs the police car to catch the speeder, that means, we have to find at which time the position of both cars is the same. So we have to equalize both equations and obtain "t".
Position of speeder = position of the police car
X0 + v*t = X0 + v0*t +1/2*a*t²
Both cars have the same initial postion (X0) and the police car starts from rest (v0 = 0). Then:
v*t = 1/2*a*t² (multiplying both sides by 2)
2v*t = a * t² (dividing both sides by a*t)
2v/a = t
Now, we replace with the data that give us the problem:
2(25.1 m/s) / 2.56 m/s² = t
<u>19.6 s = t</u>
