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

The child has greater acceleration because he/she has less mass, therefore it takes less force to move him/her. Because the child is 1/2 your size, the child has 2 times your acceleration. For instance, if one object is 10 kg and the other is 20 kg, and a 40 N force is applied to both, we can use the acceleration formula to find out each object's acceleration.

a = F/m   Acceleration formula
a = 40/10   Substitute for the 10 kg object
a = 4 m/s²   Divide to get the acceleration

a = 40/20   Substitute for the 20 kg object
a = 2 m/s²   Divide

As we can see, the 10 kg object, which is 1/2 the mass of the 20 kg object, has 2 times more acceleration than the 20 kg object because 2 x 2 = 4.

Hope this helps!