Answer:
2667 N
Explanation:
Method 1: Impulse
We can solve this problem by using the impulse formula.
- FΔt = mΔv
- Δt = time interval, m = mass of the car (kg), Δv = change in velocity
We have three known variables, so we can solve for the fourth: F.
Divide Δt from both sides to isolate F.
Substitute known values into the equation.
- F = [(1200 kg)(10 m/s - 0 m/s)] / 4.5 s
- F = [(1200)(10)]/4.5
- F = 12000/4.5
- F = 2666.666667 N
The force that the car's tires exert on the road is 2667 N.
Method 2: Newton's Second Law
The force that the car's tires exert on the road is equivalent to the force that the road exerts on the car due to Newton's Third Law of Motion.
We can calculate the force that the car's tires exert on the road by using the formula F = ma, which was derived from Newton's Second Law of Motion.
- F = ma
- F = force exerted on the car, m = mass of the car (kg), a = acceleration of the car (m/s²)
We are given the mass of the car, velocity of the car, and the time in which it accelerated.
We can use this equation for acceleration:
- a = Δv/Δt
- Δv = final velocity - initial velocity (change in velocity), Δt = time interval
The car started from rest, meaning it had an initial velocity of 0 m/s. Its final velocity was 10 m/s. The time that it took for the car to go from 0 m/s to 10 m/s was 4.5 seconds.
- a = (10 m/s - 0 m/s) / 4.50 s
- a = 10/4.5
- a = 2.222... m/s²
Now we have two known variables, mass and acceleration. We can solve for the force exerted on the car (and thus, the force the car exerts on the road) using the formula F = ma.
- F = ma
- F = (1200 kg)(2.222... m/s²)
- F = 1200 · 2.222...
- F = 2666.666667 N
The force that the car's tires exert on the road is 2667 N.
