A car with a mass of 3200 kg and a velocity of 50 m/s brakes to a final velocity of 25m/s in a distance of 85 m. what is the force the brakes apply to stop the car.
To find the force the brakes apply to stop the car, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
First, let's find the acceleration of the car by using the formula for average acceleration:
a = (final velocity - initial velocity) / time
Given that the initial velocity (u) is 50 m/s and the final velocity (v) is 25 m/s, we can substitute these values into the formula:
a = (25 - 50) / time
However, we don't have the time information in this question. Instead, we are given the distance (s) over which the car brakes. We can calculate the time by using the formula:
time (t) = distance (s) / initial velocity (u)
Given that the distance (s) is 85 m and the initial velocity (u) is 50 m/s, we can calculate the time:
t = 85 / 50
Now that we have the time (t), we can substitute this value back into the formula for acceleration:
a = (25 - 50) / (85 / 50)
Simplifying the equation, we get:
a = -25 / (85 / 50)
Next, we can calculate the force by multiplying the mass (m) of the car by the acceleration (a):
F = m * a
Substituting the given mass of the car (m) as 3200 kg and the calculated acceleration (a), we can calculate the force:
F = 3200 * (-25 / (85 / 50))