The brakes on a car permit it to decelerate at the rate of 0.80 m/s2. How much distance is required to stop this car when it is traveling at 60.0 km/hr?
Vo = 60 km/h = 60,000m/3600s. = 16.7 m/s.
V^2 = Vo^2 + 2a*d.
V = 0, Vo = 16.7 m/s, a = -0.80 m/s^2, d = ?.
To find the distance required to stop the car, we need to use the equations of motion. Specifically, we can use the equation:
v² = u² + 2as
Where:
v is the final velocity (0 m/s since the car comes to a stop),
u is the initial velocity (60.0 km/hr),
a is the acceleration (-0.80 m/s² since the car is decelerating), and
s is the distance we want to find.
First, we need to convert the initial velocity from km/hr to m/s. Since 1 km/hr is equal to 0.2778 m/s, we have:
u = 60.0 km/hr * 0.2778 m/s/km/hr = 16.67 m/s (approximately)
Now we can rearrange the equation to solve for s:
s = (v² - u²) / (2a)
Substituting the given values:
s = (0 m/s)² - (16.67 m/s)² / (2 * -0.80 m/s²) = 348.8 meters (approximately)
Therefore, it requires approximately 348.8 meters to stop the car when it is traveling at 60.0 km/hr.