Question

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

Answer 1

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:

`W=Fd`

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

`F=ma`
If we use this into the formula of the work, we get

`W=mad`

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

`2ad=v_f^2-v_i^2`
where
`v_f` and
`v_i` are the final and the initial velocity of the cart.
Re-arranging we have

`ad= (v_f^2-v_i^2)/(2)`

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

`W=mad=m (v_f^2-v_i^2)/(2) = 2.4~Kg ((10~m/s)^2-(6~m/s)^2)/(2)=76.8~J`