A car of mass 1100 kg that is traveling at 27 m/s starts to slow down and comes to a complete stop in 578 m. What is the magnitude of the braking force (in N) acting on the car?
Do what Henry did, you should get -693.685 N.
V^2 = Vo^2 + 2a*d
V = 0
Vo = 27 m/s
d = 578 m.
Solve for a. It will be negative.
F = M*a
To find the magnitude of the braking force acting on the car, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the car comes to a complete stop)
u = initial velocity (27 m/s)
a = acceleration
s = displacement (578 m)
Rearranging the equation to solve for acceleration:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (0^2 - 27^2) / (2 * 578)
Simplifying:
a = (-729) / 1156
a ≈ -0.63 m/s^2
The negative sign indicates that the car is decelerating.
Now, to find the magnitude of the braking force, we can use Newton's second law:
F = ma
Substituting the mass of the car (1100 kg) and the acceleration (-0.63 m/s^2):
F = 1100 kg * (-0.63 m/s^2)
F ≈ -693 N
The negative sign indicates that the force is acting in the opposite direction of the car's initial motion. However, since we are asked for the magnitude of the force, we ignore the negative sign and the magnitude of the braking force is approximately 693 N.