A car slows down uniformly from a speed of 20.0 m/s to rest in 7.60 s. How far did it travel in that time?
V = Vo + a*t = 0.
20 + a*7.6 = 0,
a = -2.63 m/s^2.
d =Vo*t + 0.5a*t^2 = 20*2.63 + 0.5*(-2.63)*7.6^2 =
To find the distance the car traveled, we can use the formula for distance covered during uniform acceleration:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
In this case, the car slows down uniformly from a speed of 20.0 m/s (which is the initial velocity) to rest (which means the final velocity is 0 m/s) in 7.60 s (which is the time taken).
Since the car is slowing down, the acceleration will be negative. We can calculate the acceleration using the formula:
acceleration = (final velocity - initial velocity) / time
Since the final velocity is 0 m/s, the acceleration can be calculated as:
acceleration = (0 - 20.0) / 7.60
acceleration = -20.0 / 7.60
acceleration ≈ -2.63 m/s²
Now, we can substitute the known values into the distance formula:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
distance = (20.0 * 7.60) + (1/2 * -2.63 * 7.60^2)
distance = 152 + (-20.12)
distance ≈ 131.88 m
Therefore, the car traveled approximately 131.88 meters in 7.60 seconds.