Question

Ruben is driving way over the speed limit at a constant 50 m/s and passes a parked police car. In order to catch Ruben to give him a ticket, the police car accelerates at a rate of 2.44 m/s². How much time passes before Ruben is overtaken by the police car?

A. 20.49 seconds
B. 22.44 seconds
C. 25.00 seconds
D. 52.00 seconds

Answer 1

It takes approximately 40.98 seconds before Ruben is overtaken by the police car.

Step-by-step explanation:

To determine how much time passes before Ruben is overtaken by the police car, we can use the equation of motion for the police car:

x = xo + vot + 1/2 at²

Where:

x = displacement of the police car

xo = initial position of the police car (0)

vo = initial velocity of the police car (0)

a = acceleration of the police car (2.44 m/s²)

t = time

Since Ruben is driving at a constant velocity, his displacement relative to the police car will be given by:

x = v*t

Where:

x = displacement of Ruben

v = velocity of Ruben (50 m/s)

t = time

Setting the two equations equal to each other and solving for t, we can find the time it takes for the police car to catch Ruben:

v*t = 1/2 * a * t²

50*t = 1/2 * 2.44 * t²

50 = 1.22 * t

t = 50 / 1.22 = 40.9836

Therefore, it takes approximately 40.98 seconds before Ruben is overtaken by the police car. Rounding to the nearest hundredth, the answer is 40.98 seconds.