Given:
Mass of the car (m) = 1000 kg
Initial velocity (u) = 0 m/s (since it is the initial state)
Final velocity (v) = 30 km/h = 8.33 m/s
Time taken (t) = 10 seconds
I) Force exerted by the engine (F):
Using the equation of motion:
v = u + at
Rearranging the equation to find acceleration (a):
a = (v - u) / t
Substituting the given values:
a = (8.33 - 0) / 10
a = 0.833 m/s^2
Now, using Newton's second law of motion:
F = ma
Substituting the mass and acceleration values:
F = 1000 kg * 0.833 m/s^2
F ≈ 833 N
Therefore, the force exerted by the engine is approximately 833 N.
II) Power in kilowatts (P):
Power (P) is defined as the rate at which work is done or energy is transferred. It is given by:
P = F * v
Converting the velocity from m/s to km/h:
v = 8.33 m/s * (3600/1000) km/h ≈ 30 km/h
Converting the power from watts to kilowatts:
P = F * v / 1000 ≈ 833 N * 30 km/h / 1000
P ≈ 24.99 kW
Therefore, the power of the car's engine is approximately 24.99 kilowatts.
A car of mass 1000kg is driven from its initial state with uniform acceleration and reaches a speed of 30km/h in 10 seconds.find (I)force exerted by the engine (Ii) the power in kilowatts
3 answers
The speed is not constant so the power is not constant during the acceleration
The work done during the trip is the force (constant) times the distance.
work in = 833 Newtons * d (meters) in Joules
where d = (1/2) a t^2 = (1/2)(0.833) (100)
so work in = 833 ( .833) (50) Joules
average power = work in / time = 833 * .833 * 5
The work done during the trip is the force (constant) times the distance.
work in = 833 Newtons * d (meters) in Joules
where d = (1/2) a t^2 = (1/2)(0.833) (100)
so work in = 833 ( .833) (50) Joules
average power = work in / time = 833 * .833 * 5
Apologies for the incorrect response earlier. You're correct in noting that the speed is not constant, and therefore the power is not constant during the acceleration.
To calculate the average power during the acceleration:
Given:
Force (F) = 833 N (calculated earlier)
Distance traveled during the acceleration (d) = (1/2) * a * t^2 = (1/2) * 0.833 * (10)^2 = 41.65 m (distance traveled during the 10 seconds of acceleration)
Work done during the trip:
Work = Force * Distance = 833 N * 41.65 m = 34,646.45 Joules
Average power:
Average Power = Work / Time = 34,646.45 J / 10 s = 3,464.645 Watts
Converting the average power to kilowatts:
Average Power = 3,464.645 W = 3.464645 kW
Therefore, the average power exerted by the engine during the acceleration is approximately 3.464645 kilowatts.
To calculate the average power during the acceleration:
Given:
Force (F) = 833 N (calculated earlier)
Distance traveled during the acceleration (d) = (1/2) * a * t^2 = (1/2) * 0.833 * (10)^2 = 41.65 m (distance traveled during the 10 seconds of acceleration)
Work done during the trip:
Work = Force * Distance = 833 N * 41.65 m = 34,646.45 Joules
Average power:
Average Power = Work / Time = 34,646.45 J / 10 s = 3,464.645 Watts
Converting the average power to kilowatts:
Average Power = 3,464.645 W = 3.464645 kW
Therefore, the average power exerted by the engine during the acceleration is approximately 3.464645 kilowatts.
1 answer