How much work is needed to increase the speed of a 2.4 kg cart from 6.0m/s to 10.0m/s?

Hello

1) The work W is calculated as the product between the force F applied to the cart and the distance d covered by the cart:


2) The force is the product of the mass  m of the cart and its acceleration a:

If we use this into the formula of the work, we get


3) The cart is moving by accelerated motion. For this kind of motion, we have the following relationship:

where  and  are the final and the initial velocity of the cart. 
Re-arranging we have


4) Therefore, we can subsitute  into the original formula of the work, and we get