Calculating the Distance Traveled by a Car
Question:
A car moving with an initial speed of 16 meters per second is brought to rest uniformly in 4.0 seconds. How far does the car travel during this 4.0-second interval?
Answer:
The car travels 64 meters.
Calculating the Distance Traveled by a Car
When the car is brought to rest uniformly, it means that its initial speed decreases to zero at a constant rate. To find the distance traveled by the car during this interval, we can use the formula:
d = v0t + 0.5at2
where:
d = distance traveled
v0 = initial speed = 16 m/s
t = time interval = 4.0 seconds
a = acceleration (negative value as the car is decelerating)
Given that the initial speed of the car is 16 m/s and it comes to rest in 4.0 seconds, we can calculate the acceleration using the formula:
a = (v - v0) / t
a = (0 - 16) / 4.0 = -4 m/s2
Substitute the values of v0, t, and a into the distance formula:
d = 16(4.0) + 0.5(-4)(4.0)2
d = 64 meters
Therefore, the car travels a distance of 64 meters during the 4.0-second interval while being brought to rest uniformly.