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
been there, done that
To calculate the answers to these questions, we can use the basic equations of motion. Let's go step by step:
1) To find the acceleration of the car, we can use the formula:
acceleration (a) = (final velocity - initial velocity) / time
Here, the final velocity is given as 54 km/h. However, it's better to convert it to meters per second (m/s) for consistent units. So let's convert it first:
final velocity = 54 km/h = (54 * 1000) / 3600 = 15 m/s
The initial velocity is given as rest, which means it is 0 m/s.
The time taken is given as 5 seconds.
Now we can substitute these values into the formula:
acceleration = (15 - 0) / 5 = 3 m/s^2
Therefore, the acceleration of the car is 3 m/s^2.
2) To calculate the gain in kinetic energy (k.e) of the car, we can use the formula:
gain in k.e = (1/2) * mass * (final velocity^2 - initial velocity^2)
Here, the mass of the car is given as 1000 kg.
The initial velocity is 0 m/s.
The final velocity is 15 m/s (as calculated in the previous step).
Now we can substitute these values into the formula:
gain in k.e = (1/2) * 1000 * (15^2 - 0^2) = 112,500 Joules
Therefore, the gain in kinetic energy of the car is 112,500 Joules.
3) To find the average power of the engine, we can use the formula:
average power = gain in k.e / time
Here, the gain in k.e is 112,500 Joules (as calculated in the previous step).
The time taken is 5 seconds.
Now we can substitute these values into the formula:
average power = 112,500 / 5 = 22,500 Watts
Therefore, the average power of the engine during this period is 22,500 Watts.
Note: It's important to remember that these calculations neglect friction, so in real-world scenarios, the values may differ.