During a race, you observe a 1500 kg car accelerate from an initial speed of 30m / s to a final speed of 60m / s Given this information, which of the following equations would be most useful for determining the work done accelerating the car?
The correct answer and explanation is:
Correct Answer:
The most useful equation for determining the work done accelerating the car is:
Work = ΔKinetic Energy = (1/2)mv²_final − (1/2)mv²_initial
Explanation:
To determine the work done in accelerating a car, the most relevant concept is the work-energy principle. This principle states that the net work done on an object is equal to the change in its kinetic energy.
Kinetic energy is the energy an object possesses due to its motion and is given by the formula:
Kinetic Energy (KE) = (1/2)mv²,
where m is the mass of the object and v is its velocity.
In this case, the car has a mass of 1500 kg, an initial speed of 30 m/s, and a final speed of 60 m/s. Since the force and distance involved in the acceleration are not given, using the kinematic or force-based work formulas such as Work = Force × Distance × cos(θ) would not be appropriate or useful. Instead, focusing on the change in kinetic energy provides a direct path to calculating the work done.
The change in kinetic energy (ΔKE) is:
ΔKE = (1/2) * m * v²_final − (1/2) * m * v²_initial
ΔKE = (1/2)(1500)(60)² − (1/2)(1500)(30)²
ΔKE = (1/2)(1500)(3600 − 900)
ΔKE = (750)(2700)
ΔKE = 2,025,000 joules
This result means that 2,025,000 joules of work was done to increase the car’s speed from 30 m/s to 60 m/s.
Therefore, the most useful equation is:
Work = (1/2)mv²_final − (1/2)mv²_initial
This equation directly links the car’s mass and velocity to the amount of work performed.