A motor car of mass 2000kg accelerates from rest at 3 ms-2 for 4s on a straight road. find the average useful output power of the engine of the car.
Find the change in kinetic energy in Joules and divide by 4 seconds to get average power.
v = a t = 3(4) = 12 m/s final
so
Ke = (1/2)(2000)(144) Joules
power = Ke/4 Watts
To find the average useful output power of the engine of the car, we need to calculate the work done by the engine and divide it by the time taken.
Step 1: Calculate the work done.
The work done on an object is given by the formula work = force * distance.
In this case, the force is the driving force generated by the engine, and the distance is the displacement of the car.
To find the force, we can use Newton's second law of motion: force = mass * acceleration.
Given that the mass of the car is 2000 kg and the acceleration is 3 m/s^2, we can calculate the force.
force = 2000 kg * 3 m/s^2 = 6000 N.
Now, let's find the distance traveled by the car.
Given that the car starts from rest, we can use the equation of motion: distance = (initial velocity * time) + (0.5 * acceleration * time^2).
The initial velocity is zero, and the time is 4 seconds.
distance = 0 + (0.5 * 3 m/s^2 * (4s)^2) = 0 + (0.5 * 3 m/s^2 * 16s^2) = 0 + 24m = 24m.
The work done by the engine is work = force * distance = 6000 N * 24 m = 144,000 Nm (Joules).
Step 2: Calculate the average useful output power.
Power is the rate at which work is done, and it is given by the formula power = work / time.
The time taken is 4 seconds.
Therefore, the average useful output power of the engine of the car is power = 144,000 J / 4s = 36,000 Watts (W).