Question:
A car is traveling along a straight road. At time t = 0, the car starts from rest and accelerates uniformly at a rate of 2 m/s^2 for a total of 4 seconds.
a) What is the final velocity of the car at the end of the 4 seconds? b) How far does the car travel during the 4 seconds?
Answer:
a) To find the final velocity, we can use the formula:
v = u + at
where: v = final velocity u = initial velocity (which is 0 in this case) a = acceleration (2 m/s^2) t = time (4 seconds)
Substituting the given values into the formula:
v = 0 + (2 m/s^2)(4 s) v = 8 m/s
Therefore, the final velocity of the car at the end of the 4 seconds is 8 m/s.
b) To find the distance traveled by the car, we can use the formula:
s = ut + (1/2)at^2
where: s = distance u = initial velocity (which is 0 in this case) a = acceleration (2 m/s^2) t = time (4 seconds)
Substituting the given values into the formula:
s = 0(4 s) + (1/2)(2 m/s^2)(4 s)^2 s = (1/2)(2 m/s^2)(16 s^2) s = 16 m
Therefore, the car travels a distance of 16 meters during the 4 seconds.