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
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.
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
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 find the force exerted by the engine on the car, we need to find the acceleration first. We can use the following equation:
v = u + at
Where:
v = final velocity = 30 km/h = 8.33 m/s (1 km/h = 0.2778 m/s)
u = initial velocity = 0 m/s
t = time = 10 seconds
Rearranging the equation, we get:
a = (v - u) / t
Substituting the values, we get:
a = (8.33 m/s - 0 m/s) / 10 s
a = 0.83 m/s²
Now, we can find the force exerted by the engine using Newton's second law:
F = ma
Where:
F = force exerted by the engine (unknown)
m = mass of the car = 1000 kg
a = acceleration = 0.83 m/s²
Substituting the values, we get:
F = 1000 kg * 0.83 m/s²
F = 830 N
Therefore, the force exerted by the engine is 830 Newtons.
Now, to find the power in kilowatts, we can use the following equation:
Power = force * velocity
Where:
Power = power in watts (unknown)
force = force exerted by the engine = 830 N
velocity = final velocity = 30 km/h = 8.33 m/s (as calculated before)
Converting the power from watts to kilowatts, we divide by 1000:
Power = (force * velocity) / 1000
Substituting the values, we get:
Power = (830 N * 8.33 m/s) / 1000
Power = 6.90 kilowatts
Therefore, the power exerted by the engine is 6.90 kilowatts.
To find the force exerted by the engine on the car, we can use Newton's second law of motion, which states that the force exerted on an object is equal to its mass multiplied by its acceleration:
Force = Mass × Acceleration
In this case, the car has a mass of 1000 kg. To find the acceleration, we can use the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Since the car starts from rest, the initial velocity is 0. The final velocity is given as 30 km/h, but we need to convert it to meters per second (m/s) to match the units of the other quantities.
1 km/h = 1000 m/3600 s = 10/36 m/s
Thus, 30 km/h = (30 × 10/36) m/s = 300/36 m/s ≈ 8.33 m/s
Plugging in these values, we have:
Acceleration = (8.33 m/s - 0 m/s) / 10 s = 0.833 m/s^2
Now we can calculate the force exerted by the engine:
Force = Mass × Acceleration = 1000 kg × 0.833 m/s^2 = 833 N
Therefore, the force exerted by the engine is 833 Newtons.
To find the power in kilowatts, we can use the formula:
Power = Force × Velocity
However, the velocity in this formula should be in meters per second (m/s), so we need to convert the velocity from km/h to m/s as we did before:
30 km/h ≈ 8.33 m/s
Plugging in the values, we have:
Power = Force × Velocity = 833 N × 8.33 m/s ≈ 6950.89 watts
To convert watts to kilowatts, we divide by 1000:
Power (in kilowatts) = 6950.89 watts / 1000 = 6.95 kilowatts
Therefore, the power of the engine is 6.95 kilowatts.