Kinetic energy and work energy thereom

[amannaan2000]

a 5.75 kg object is initially moving so that its x-component of velocity is 6.00m/s and its y-component is -2.00m/s. what is the kinetic energy of the object at this time. What is the change of kinetic energy do that its velocity is 8.50m/s in the x direction and 5.00m/s in the y direction

 

[Perillux]

kinetic energy equals (1/2)m*v^2
You already know the mass and the 2 components of velocity, just use pythagorean theorem to find the actual velocity.

and since mass can't change, then change in kinetic energy is equal to (1/2)m*(change in velocity)^2

 

[St. Aegis]

As perillux said, you use the pythagorean theorem to find the total velocity magnitude and use that and the given mass in the formula to get the answer.

 

[Doc Al]

and since mass can't change, then change in kinetic energy is equal to (1/2)m*(change in velocity)^2

Careful. This is incorrect.

$$\Delta {KE} = 1/2m\Delta(v^2) \ne 1/2m(\Delta v)^2$$