A car of mass 1000 kg accelerates uniformly from rest to a velocity of 54 km/h in 5 seconds calculate 1) its acceleration 2) its gain in k.e 3) average power of the engine during this period . neglect friction
54 km/h * (1 h/3600 s)*(1000 m/km)
= 15 m/s
15 m/s / 5 s = 3 m/s^2
(1/2) m v^2 Joules
(1/2) m v^2 Joules/15seconds ---> Watts
To answer each question, we'll need to use the relevant physics equations and formulas. Let's go step by step:
1) Calculating the acceleration:
To find the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity is 0 (since the car starts from rest), the final velocity is 54 km/h, and the time is 5 seconds. However, we first need to convert the final velocity from km/h to m/s, as the SI unit for acceleration is meters per second squared (m/s^2).
Converting 54 km/h to m/s:
54 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 15 m/s
Now we can plug the values into the formula:
acceleration = (15 m/s - 0 m/s) / 5 s
acceleration = 3 m/s^2
Therefore, the acceleration of the car is 3 m/s^2.
2) Calculating the gain in kinetic energy:
The kinetic energy of an object is given by the formula:
kinetic energy = (1/2) * mass * velocity^2
In this case, the mass of the car is 1000 kg, and the initial velocity is 0 m/s (since the car starts from rest). The final velocity is 15 m/s, as we calculated before.
Plugging the values into the formula:
initial kinetic energy = (1/2) * 1000 kg * (0 m/s)^2 = 0 J
final kinetic energy = (1/2) * 1000 kg * (15 m/s)^2 = 112,500 J
The gain in kinetic energy is the difference between the final and initial kinetic energy:
gain in kinetic energy = final kinetic energy - initial kinetic energy = 112,500 J - 0 J = 112,500 J
Therefore, the gain in kinetic energy of the car is 112,500 J.
3) Calculating the average power of the engine:
Power is defined as the rate at which work is done. The formula for power is:
power = work / time
In this case, we need to find the work done by the engine. The work done is equal to the change in kinetic energy (since no other work or forces are involved, neglecting friction).
The work done is given by:
work = gain in kinetic energy = 112,500 J
The time is given as 5 seconds.
Plugging the values into the formula:
average power = work / time = 112,500 J / 5 s
average power = 22,500 W
Therefore, the average power of the car's engine during this period is 22,500 Watts.