The brakes are applied to a car traveling on a dry, level highway. A typical value for the magnitude of the car's acceleration is 4.75 m/s2. If the car's initial speed is 32.1 m/s, how long does it take to stop and how far does it travel, starting from the moment the brakes are applied?
time to stop:
stopping distance:
the
To find the time it takes for the car to stop and the stopping distance, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, because the car stops)
u = initial velocity (32.1 m/s)
a = acceleration (-4.75 m/s^2, negative because it opposes the initial motion of the car)
s = stopping distance (unknown)
Now, rearranging the equation, we have:
s = (v^2 - u^2) / (2a)
Substituting the given values:
s = (0^2 - 32.1^2) / (2 * -4.75)
Calculating:
s = (-1029.21) / (-9.5)
s = 108.07 meters
Thus, the stopping distance of the car is approximately 108.07 meters.
Next, to find the time it takes for the car to stop, we can use the equation:
v = u + at
Where:
v = final velocity (0 m/s)
u = initial velocity (32.1 m/s)
a = acceleration (-4.75 m/s^2, negative because it opposes the initial motion of the car)
t = time (unknown)
Rearranging the equation, we have:
t = (v - u) / a
Substituting the given values:
t = (0 - 32.1) / (-4.75)
Calculating:
t = (-32.1) / (-4.75)
t = 6.76 seconds
Therefore, it takes approximately 6.76 seconds for the car to stop after the brakes are applied.