/sci/ - Science & Math

>>10873150
Take F=ma, OP.

Suppose I apply the same force on each, 2 newtons. This force applied to the first one accelerates by 2m/s^2, so in 1 second it reaches the speed I want. On the second one, 2=4a, so a = 1/2 s^2, thus it takes 2 seconds for it to reach 1 m/s. 1:2, hence your confusion.

However, energy = work = F x d, and not energy = F x t. Why is it times distance? Intuitively, I understand that it is because the effect is Spatial, not Temporal, and while it takes me longer, in seconds, to accelerate the second body the distance displaced is the same( V^2 = 2ad ). Because of physical symmetry, this distance is equal to the displacement when decelerating the body with a -2 newton force. So when concerned with the spatial consequences of a movement, it makes sense to think of energy as force x distance and not time.