A car accelerates uniformly from rest to a speed of 50.9 km/h (14.1 m/s) in 8 s. Find the distance the car travels during this time.
constant acceleration so
a = change in speed / time
a = 14.1/8 m/s^2
again like the last problem
d = (1/2) a t^2
d = .5 * a * (64)
To find the distance the car travels during this time, we can use the equation:
distance = initial velocity * time + 0.5 * acceleration * time^2
In this case, the car starts from rest, so the initial velocity is 0. The final velocity is 14.1 m/s and the time is 8 seconds.
First, let's convert the final velocity from km/h to m/s:
final velocity = 50.9 km/h = 50.9 * 1000 / 3600 = 14.14 m/s (rounded to two decimal places)
Now we can substitute the values into the equation:
distance = 0 * 8 + 0.5 * acceleration * 8^2
Since the car accelerates uniformly, we can find the acceleration by using the formula:
acceleration = (final velocity - initial velocity) / time
Substituting the values, we get:
acceleration = (14.14 - 0) / 8 = 1.77 m/s^2 (rounded to two decimal places)
Now we can find the distance:
distance = 0 * 8 + 0.5 * 1.77 * 8^2
distance = 0 + 0.5 * 1.77 * 64
distance ≈ 56.77 meters (rounded to two decimal places)
Therefore, the car travels approximately 56.77 meters during this time.