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: [tex]W=Fd[/tex]
2) The force is the product of the mass m of the cart and its acceleration a: [tex]F=ma[/tex] If we use this into the formula of the work, we get [tex]W=mad[/tex]
3) The cart is moving by accelerated motion. For this kind of motion, we have the following relationship: [tex]2ad=v_f^2-v_i^2[/tex] where [tex]v_f[/tex] and [tex]v_i[/tex] are the final and the initial velocity of the cart. Re-arranging we have [tex]ad= \frac{v_f^2-v_i^2}{2} [/tex]
4) Therefore, we can subsitute [tex]ad[/tex] into the original formula of the work, and we get [tex]W=mad=m \frac{v_f^2-v_i^2}{2} = 2.4~Kg \frac{(10~m/s)^2-(6~m/s)^2}{2}=76.8~J [/tex]
