Infer you and a child are on skates and you give each other a push. if the mass of the child is half of your mass, who has a greater acceleration ? by what factor?

Hello! 

Here is a conservation of momentum problem. If we have two masses and one is twice the other, 1kg and 2kg, and momentum is equal to mass*velocity.
Velocity=acceleration*time so subbing in we get 

p(momentum)=m*a*t so now setting p1 and p2 equal to each other we get 

p=m1*a1*t1 = m2*a2*t2 so we can see a linear relationship here and the only difference is mass is 2x so that means the lighter 1/2mass child will accelerate faster by a factor of 2 than 2xmass child.

Or we can just look at newtons second law and see the relationship there. 

F=ma so we can see the force would go up by a factor of 2 resulting in an acceleration increase of a factor of 2. 

Hope this helps. Any questions please just ask! Thank you so much!