Need Physics Help: Acceleration of a Cart w/ Working Out

[deluxenathan]

Need Physics help urgent!

A man pushes an empty 20kg cart as hard as he can and the cart accelerates at 10m/s. The cart is then filled so that the weight is 100kg. How much acceleration can the man achieve pushing the full cart? (Show all your working)

Hi that's the question i need to do I've done most of the working out i just don't understand the algebra in it and where it goes so if someone could fill and algebra out for me that would be great

ive added a attachment with the working out I've done so far.

 

[HallsofIvy]

You have two different accelerations so call them a and a'. You have F= ma and F= (5m)a'. F and m are the same.

 

[Lobezno]

He has acceleration as different, in the attachment at least.

It's fine what you're doing so far, but in my head, it works better by finding the force using Newton's Second:

F=ma -> F=20*10

Then you can plug it into any other equation as the force value, and you can get acceleration for a known mass (or mass for a known acceleration).