A 1200.0-kg car speeds up from 16.0 m/s to 20.0 m/s. How much work was done on the car to increase its speed?

yes yes

very bad

To calculate the work done on the car to increase its speed, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy.

The formula for calculating work is given by:

Work = ΔKE = (1/2) * m * (v^2 - u^2)

Where:
ΔKE is the change in kinetic energy
m is the mass of the car (1200.0 kg in this case)
v is the final velocity (20.0 m/s)
u is the initial velocity (16.0 m/s)

Let's plug in the values and calculate:

Work = (1/2) * 1200.0 kg * [ (20.0 m/s)^2 - (16.0 m/s)^2 ]

Work = (1/2) * 1200.0 kg * [ 400.0 m^2/s^2 - 256.0 m^2/s^2 ]

Work = (1/2) * 1200.0 kg * 144.0 m^2/s^2

Work = 86400 J

Therefore, the work done on the car to increase its speed is 86400 Joules.

To determine the work done on the car to increase its speed, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.

The formula for calculating work is:
Work = Force × Distance × Cos(θ)

In this case, the force applied to the car is the net force acting on it, which is caused by the acceleration. The distance over which the force is applied is not provided, but since the force is constant, we can assume that the distance is not a factor in this problem. Therefore, we can disregard the distance and focus solely on the change in kinetic energy.

The formula for kinetic energy is given by:
Kinetic Energy = (1/2) × mass × velocity^2

We can use this formula to calculate the change in kinetic energy (ΔKE) by subtracting the initial kinetic energy from the final kinetic energy.

ΔKE = KE_final - KE_initial

To calculate the initial kinetic energy, we use the mass and initial velocity:
KE_initial = (1/2) × mass × velocity_initial^2

Substituting the given values:
mass = 1200.0 kg
velocity_initial = 16.0 m/s

KE_initial = (1/2) × 1200.0 kg × (16.0 m/s)^2

Similarly, we can calculate the final kinetic energy using the mass and final velocity:
KE_final = (1/2) × mass × velocity_final^2

Substituting the given values:
velocity_final = 20.0 m/s

KE_final = (1/2) × 1200.0 kg × (20.0 m/s)^2

Finally, we can find the change in kinetic energy and hence the work done on the car:
ΔKE = KE_final - KE_initial

Work = ΔKE

Substituting the calculated values, we can find the work done on the car.