Forces and energy

SgStudentStressed SG

net F=ma so if a boy runs at me with a 2m/s2 acceleration with 10m/s velocity while another boy of same mass runs at the same acc but now with 20m/s volocity. they would both have the same amount of force right? but then if i were to stop the 20m/s boy, it would be more difficult.

if we take energy, KE=1/2mv2. if their masses are 10kg (ikr) then 20m/s boy have more energy comapred to the 10m/s boy. so what is the link between force and energy in this case? thanks

eagle SG

I don't understand your question. It is very messy.

F = ma, so something with a larger m will get a smaller a if we apply the same force. Hence, it is not more difficult to stop something with larger velocity. The a is smaller, so it takes a longer time to stop something with higher velocity since v = u + at.

In terms of energy, E = Fd. So you would the faster object (with same mass and hence more KE) would stop over a longer distance.