what is the average force needed to stop a car (1000kg) traveling 28m/s in 55m?
To find the average force needed to stop a car, you can use Newton's second law, which states that force is equal to mass multiplied by acceleration (F = m * a). In this case, we need to find the acceleration first.
To calculate the acceleration, you can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.
Given:
Mass (m) = 1000 kg
Initial velocity (u) = 28 m/s
Distance traveled (s) = 55 m
1. Calculate the final velocity (v):
Using the equation v^2 = u^2 + 2as, plug in the given values and solve for v.
v^2 = (28 m/s)^2 + 2 * a * 55 m
v^2 = 784 m^2/s^2 + 110 a m
Since the car is coming to a stop, the final velocity is 0, so the equation becomes:
0 = 784 m^2/s^2 + 110 a m
2. Solve for acceleration (a):
0 = 784 m^2/s^2 + 110 a m
- 784 m^2/s^2 = 110 a m
a = - 784 m^2/s^2 / 110 m
a ≈ - 7.13 m/s^2
The negative sign indicates that the car is decelerating.
3. Calculate the average force (F):
Now that we have the acceleration, we can use Newton's second law to calculate the force.
F = m * a
F = 1000 kg * (-7.13 m/s^2)
F ≈ -7130 N
The average force needed to stop the car is approximately 7130 N. The negative sign indicates that the force is opposing the car's initial motion, serving to stop it.