A car accelerates uniformly from rest to a
speed of 24.2 km/h in 5.1 s.
Find the distance it travels during this time.
Answer in units of m
24.2 / 5.1 =
123.42 m
To find the distance traveled by the car, we need to use the formula for distance traveled during uniform acceleration:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
In this case, the car starts from rest, so the initial velocity is 0 km/h. The final velocity is 24.2 km/h, but we need to convert km/h to m/s to use consistent units in the formula. The conversion factor is 1 km/h = 0.27778 m/s.
Converting the initial velocity:
initial velocity = 0 km/h = 0 m/s
Converting the final velocity:
final velocity = 24.2 km/h * 0.27778 m/s = 6.722 m/s
The time given is 5.1 s.
Since the car starts from rest, the acceleration is given by the formula:
acceleration = (final velocity - initial velocity) / time
Substituting the values:
acceleration = (6.722 m/s - 0 m/s) / 5.1 s = 1.317 m/s^2
Now we can calculate the distance traveled:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
distance = (0 m/s * 5.1 s) + (0.5 * 1.317 m/s^2 * (5.1 s)^2)
distance = 0 + 3.366 m
Therefore, the car travels a distance of 3.366 m during this time.