A 250 kg car starting from rest is pushed 30m. When the car reaches 30m, it’s traveling at a speed of 12m/s and it encounters 52N of friction. What is the acceleration of the car and what is the force of the push on the car?
During the period it is accelerating without friction, V = sqrt(2 a X)
Solve for acceleration a.
The pushing force during that time is
F = m a
You have not made it clear at what time you want to know the acceleration, Is it before or after friction is applied?
To find the acceleration of the car, we can use the equation of motion:
Fnet = ma
where Fnet is the net force acting on the car, m is the mass of the car, and a is the acceleration. The net force is the sum of the force of the push and the force of friction:
Fnet = Fpush - Ffriction
Given that the force of friction is 52N and the mass of the car is 250 kg, we can substitute these values into the equation:
52N = Fpush - Ffriction
52N = Fpush - 52N
Simplifying the equation, we get:
104N = Fpush
So the force of the push on the car is 104N.
Next, let's find the acceleration of the car. We can use the equation of motion:
vf^2 = vi^2 + 2ad
where vf is the final velocity (12 m/s in this case), vi is the initial velocity (0 m/s as the car starts from rest), a is the acceleration, and d is the distance traveled (30m in this case).
Substituting the given values into the equation, we get:
(12 m/s)^2 = (0 m/s)^2 + 2a(30 m)
Simplifying, we have:
144 m^2/s^2 = 60a
Dividing both sides by 60:
2.4 m/s^2 = a
Therefore, the acceleration of the car is 2.4 m/s^2.