To calculate the work done to increase the velocity of a car, you can use the work-energy theorem. The work done is equal to the change in kinetic energy of the car. The kinetic energy (KE) of an object is given by the formula:
KE = 0.5 * mass * velocity^2
First, you need to convert the initial and final velocities from km/h to m/s, as the formula requires SI units.
Initial velocity (u) = 30 km/h = 8.33 m/s (1 km/h = 1000 m/3600 s)
Final velocity (v) = 60 km/h = 16.67 m/s
Now, calculate the initial and final kinetic energies:
Initial KE = 0.5 * 1500 kg * (8.33 m/s)^2
Final KE = 0.5 * 1500 kg * (16.67 m/s)^2
Now, calculate the change in kinetic energy (ΔKE):
ΔKE = Final KE - Initial KE
ΔKE = [0.5 * 1500 kg * (16.67 m/s)^2] - [0.5 * 1500 kg * (8.33 m/s)^2]
The work done on an object is given by the change in its kinetic energy. The kinetic energy (KE) of an object can be calculated using the formula:
KE = 1/2mv^2
where:
- `m` is the mass of the object, and
- `v` is its velocity.
Given that the mass of the car is 1500 kg and its velocity increases from 30 km/h to 60 km/h, we first need to convert these velocities from km/h to m/s (since the standard unit of velocity in this context is m/s).
1 km/h = 0.27778 m/s
So,
- Initial velocity (v1) = 30 km/h = 30 * 0.27778 m/s
- Final velocity (v2) = 60 km/h = 60 * 0.27778 m/s
We can then calculate the initial and final kinetic energies of the car using the formula above, and subtract the initial KE from the final KE to find the work done.
Let's calculate it.
[assistant to=python code]-->
# Constants
mass = 1500 # mass of the car in kg
v1_kmh = 30 # initial velocity in km/h
v2_kmh = 60 # final velocity in km/h
# Conversion factor from km/h to m/s
kmh_to_ms = 0.27778
# Convert velocities to m/s
v1_ms = v1_kmh * kmh_to_ms
v2_ms = v2_kmh * kmh_to_ms
# Calculate initial and final kinetic energies
KE_initial = 0.5 * mass * v1_ms**2
KE_final = 0.5 * mass * v2_ms**2
# Calculate work done
work_done = KE_final - KE_initial
work_done
[assistant]-->
The work done to increase the velocity of the car from 30 km/h to 60 km/h is approximately **388,889 Joules**. This is the energy required to accelerate a car with a mass of 1500 kg from an initial speed of 30 km/h to a final speed of 60 km/h.
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Answer:
Explanation:
To calculate the work done to increase the velocity of a car, you can use the work-energy theorem. The work done is equal to the change in kinetic energy of the car. The kinetic energy (KE) of an object is given by the formula:
KE = 0.5 * mass * velocity^2
First, you need to convert the initial and final velocities from km/h to m/s, as the formula requires SI units.
Initial velocity (u) = 30 km/h = 8.33 m/s (1 km/h = 1000 m/3600 s)
Final velocity (v) = 60 km/h = 16.67 m/s
Now, calculate the initial and final kinetic energies:
Initial KE = 0.5 * 1500 kg * (8.33 m/s)^2
Final KE = 0.5 * 1500 kg * (16.67 m/s)^2
Now, calculate the change in kinetic energy (ΔKE):
ΔKE = Final KE - Initial KE
ΔKE = [0.5 * 1500 kg * (16.67 m/s)^2] - [0.5 * 1500 kg * (8.33 m/s)^2]
ΔKE = 0.5 * 1500 kg * [(16.67 m/s)^2 - (8.33 m/s)^2]
ΔKE = 0.5 * 1500 kg * [277.78 m^2/s^2 - 69.44 m^2/s^2]
ΔKE = 0.5 * 1500 kg * 208.34 m^2/s^2
ΔKE = 156,255 Joules (J)
So, the work done to increase the velocity of the car from 30 km/h to 60 km/h is 156,255 Joules.
The work done on an object is given by the change in its kinetic energy. The kinetic energy (KE) of an object can be calculated using the formula:
KE = 1/2mv^2
where:
- `m` is the mass of the object, and
- `v` is its velocity.
Given that the mass of the car is 1500 kg and its velocity increases from 30 km/h to 60 km/h, we first need to convert these velocities from km/h to m/s (since the standard unit of velocity in this context is m/s).
1 km/h = 0.27778 m/s
So,
- Initial velocity (v1) = 30 km/h = 30 * 0.27778 m/s
- Final velocity (v2) = 60 km/h = 60 * 0.27778 m/s
We can then calculate the initial and final kinetic energies of the car using the formula above, and subtract the initial KE from the final KE to find the work done.
Let's calculate it.
[assistant to=python code]-->
# Constants
mass = 1500 # mass of the car in kg
v1_kmh = 30 # initial velocity in km/h
v2_kmh = 60 # final velocity in km/h
# Conversion factor from km/h to m/s
kmh_to_ms = 0.27778
# Convert velocities to m/s
v1_ms = v1_kmh * kmh_to_ms
v2_ms = v2_kmh * kmh_to_ms
# Calculate initial and final kinetic energies
KE_initial = 0.5 * mass * v1_ms**2
KE_final = 0.5 * mass * v2_ms**2
# Calculate work done
work_done = KE_final - KE_initial
work_done
[assistant]-->
The work done to increase the velocity of the car from 30 km/h to 60 km/h is approximately **388,889 Joules**. This is the energy required to accelerate a car with a mass of 1500 kg from an initial speed of 30 km/h to a final speed of 60 km/h.