Acceleration - Displacement Graph

[PhysicsStudnt]

In terms of calculus, How do i prove that the area under the acceleration time graph gives me the change in KE / mass...

Attempt at solution...

Area under the graph of a function y = f(x) is given by ∫y dx

Therefore area under acceleration displacement graph is ∫a ds (considering the function to be a=f(s))

=> ∫f/m ds

=> 1/m (∫f.ds)

=> 1/m (W) ...[work done = ∫f.ds ]

=> ΔKE/m ...[W = ΔKE]


1. Is this proof correct mathematically and theoretically...
2. Is there a different or better proof...

 

[SteamKing]

It's not clear what you are trying to do. First, you talk about the area under the acceleration-time graph, then you talk about the area under the acceleration-displacement graph.

This is why PF has a HW template and we ask all HW posters to fill out the template when asking a question. It reduces the amount of confusion, which is always lurking to pounce on the unwary.

https://www.physicsforums.com/showpost.php?p=3977513&postcount=2

Be sure to include the complete text of the original problem as stated.