Final answer:
The magnitude of the skateboard's acceleration, a, while the teenager is pushing backwards on the ground can be calculated using the expression a = (F_push - F_friction) / m, where F_push is the force exerted by the teenager pushing and F_friction is the force of friction between the skateboard and the ground.
Step-by-step explanation:
The magnitude of the skateboard's acceleration, a, while the teenager is pushing backwards on the ground can be expressed as follows:
a = F_net / m
Where F_net is the net force exerted on the skateboard and m is the mass of the skateboard. In this case, since the teenager is pushing backwards on the ground, the net force can be given by the force provided by the teenager pushing minus the force of friction between the skateboard and the ground. Therefore, the expression for the magnitude of the skateboard's acceleration, a, is:
a = (F_push - F_friction) / m