PLEASE HELP
If a car generates 18 hp when travelling at a steady 90 km/h with an average frictional force of 5.4 x 10^2 N, how much power altogether must the car supply to accelerate to 100 km/h in 5.0 s?
To determine the total power the car must supply to accelerate, we need to consider both the power needed to overcome friction at 90 km/h and the power needed to accelerate the car to 100 km/h in 5.0 seconds.
First, let's determine the power needed to overcome friction at 90 km/h. Power is defined as the rate at which work is done, and work is given by the formula W = Fd, where W is work, F is force, and d is distance. In this case, the force is the average frictional force and the distance is the distance traveled in one hour at 90 km/h.
To convert the speed from km/h to m/s, we divide by 3.6, so the speed at 90 km/h is 90/3.6 = 25 m/s. The distance traveled in one hour at 90 km/h is 25 m/s × 3600 s = 90000 m.
Then, we can calculate the work done against friction using the formula W = Fd, where F is the average frictional force and d is the distance traveled. The work done is W = (5.4 × 10^2 N) × (90000 m) = 4.86 × 10^7 J.
Now, let's determine the power needed to accelerate the car from 90 km/h to 100 km/h in 5.0 seconds. Power is also defined as the rate at which work is done. The work done to accelerate the car can be calculated using the formula W = ΔKE, where ΔKE is the change in kinetic energy.
The change in kinetic energy can be calculated using the formula ΔKE = (1/2)mv^2, where m is the mass of the car and v is the change in velocity. In this case, the change in velocity is 100 km/h - 90 km/h = 10 km/h = 10/3.6 m/s = 2.78 m/s.
Let's assume the mass of the car is 1000 kg. Then, the change in kinetic energy is ΔKE = (1/2) × (1000 kg) × (2.78 m/s)^2 = 3.86 × 10^3 J.
Now, we can calculate the total power the car must supply. The total power is given by the equation P = W/t, where P is power, W is work, and t is time. In this case, the time is 5.0 seconds.
The total power is P = (4.86 × 10^7 J + 3.86 × 10^3 J) / 5.0 s = 9.72 × 10^6 J/s = 9.72 MW.
Therefore, the car must supply a total power of 9.72 MW to accelerate to 100 km/h in 5.0 seconds.