How much work W is required to accelerat a 1000kg object from initial velocity of 100m/s to a final velocity of 200m/s?

To calculate the work required to accelerate an object, you need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. The formula for work is:

W = ΔKE

where W is the work done, and ΔKE is the change in kinetic energy.

The change in kinetic energy can be calculated using the formula:

ΔKE = 1/2 * m * (vf^2 - vi^2)

where m is the mass of the object, vf is the final velocity, and vi is the initial velocity.

Given:
Mass (m) = 1000 kg
Initial velocity (vi) = 100 m/s
Final velocity (vf) = 200 m/s

Using the formula for ΔKE, we can calculate the change in kinetic energy:

ΔKE = 1/2 * 1000 kg * (200^2 m^2/s^2 - 100^2 m^2/s^2)

Now, plug in the values and calculate ΔKE:

ΔKE = 1/2 * 1000 kg * (40000 m^2/s^2 - 10000 m^2/s^2)
= 1/2 * 1000 kg * 30000 m^2/s^2
= 15000 kg * m^2/s^2
= 15000 J (Joules)

Therefore, the work required to accelerate the object is 15000 Joules.