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

User Olanod
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1 Answer

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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
User Rishikarri
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