Final answer:
The power required to accelerate a 900-kg car from rest to a velocity of 22.22 m/s (80 km/h) in 20 seconds on a level road is calculated to be 22.22 kW.
Step-by-step explanation:
Calculating the Power Required for Acceleration
To calculate the power required to accelerate a 900-kg car from rest to a velocity of 80 km/h (which is 22.22 m/s) in 20 s on a level road, we need to use the formula for power in terms of force and velocity, as well as Newton's second law of motion (F = ma).
First, we convert the final velocity to meters per second (m/s) since the SI unit for velocity is m/s:
- 80 km/h = 80 × (1000 m / 3600 s) = 22.22 m/s
Next, we calculate the acceleration (a) needed using the formula:
a = (v - u) / t
- Where v = final velocity, u = initial velocity (0 m/s, since the car is starting from rest), and t = time taken.
- a = (22.22 m/s - 0 m/s) / 20 s = 1.111 m/s2
Now we calculate the force (F) required using Newton's second law:
F = ma
- Where m = mass of the car, and a = acceleration.
- F = 900 kg × 1.111 m/s2 = 999.9 N
Finally, we use the formula for power (P) in terms of force and velocity:
P = Fv
- P = 999.9 N × 22.22 m/s = 22,220 W or 22.22 kW
Therefore, the power required to accelerate the car is 22.22 kW.