Final answer:
It will take the car 6.41 seconds to reach a speed of 15.0 m/s, neglecting friction. If the car also climbs a 3.00-m-high hill, it will take 1.53 seconds.
Step-by-step explanation:
To calculate the time it takes for the car to reach a speed of 15.0 m/s:
- Convert the power output from horsepower to watts: 40.0 hp = 40.0 x 746 W = 29840 W
- Calculate the force required to accelerate the car: F = P/v = 29840 W / 15.0 m/s = 1989.33 N
- Use Newton's second law to calculate the acceleration: F = ma, a = F/m = 1989.33 N / 850 kg = 2.34 m/s^2
- Use the kinematic equation v = u + at to solve for the time: 15.0 m/s = 0 + 2.34 m/s^2 * t, t = 15.0 m/s / 2.34 m/s^2 = 6.41 s
To calculate the time it takes for the car to climb a 3.00-m-high hill:
- Use the equation for work done against gravity to calculate the work: W = mgh = 850 kg * 9.8 m/s^2 * 3.00 m = 24990 J
- Calculate the force required to climb the hill: F = W/d = 24990 J / 3.00 m = 8330 N
- Use Newton's second law to calculate the acceleration: F = ma, a = F/m = 8330 N / 850 kg = 9.80 m/s^2
- Use the kinematic equation v = u + at to solve for the time: 0 + 9.80 m/s^2 * t = 15.0 m/s, t = 15.0 m/s / 9.80 m/s^2 = 1.53 s