AP Physics 1 Exam Question:

A car is traveling along a straight road. Its initial velocity is 10 m/s in the positive x-direction. The car then accelerates uniformly at a rate of 2 m/s^2 for a duration of 5 seconds. Determine the final velocity of the car and the distance it traveled during this time period.

Answer:

To solve this problem, we can use the equations of motion for uniformly accelerated motion. The equations we will use are:

1. v = u + at
2. s = ut + 0.5at^2

where: v = final velocity u = initial velocity a = acceleration t = time s = distance

Given: u = 10 m/s (initial velocity) a = 2 m/s^2 (acceleration) t = 5 s (time duration)

Let's solve for the final velocity first using equation (1):

v = u + at

v = 10 m/s + 2 m/s^2 * 5 s

v = 10 m/s + 10 m/s

v = 20 m/s

The final velocity of the car is 20 m/s in the positive x-direction.

Now, let's find the distance traveled by the car during this time period, using equation (2):

s = ut + 0.5at^2

s = 10 m/s * 5 s + 0.5 * 2 m/s^2 * (5 s)^2

s = 50 m + 0.5 * 2 m/s^2 * 25 s^2

s = 50 m + 0.5 * 2 * 25 m^2/s^2

s = 50 m + 25 m

s = 75 m

The car traveled a distance of 75 meters during this time period.

Therefore, the final velocity of the car is 20 m/s and it traveled a distance of 75 meters during the 5-second time period.