(a) The manufacturers of a particular brand of car conduct head-on collision tests and find that in the absence of a passenger side air bag, a childs head (which has the mass of 3.5 kg) goes from a speed of 40 km/h relative to the dashboard just before its collision. This collision lasts just 0.08 seconds. What is the average force exerted on the childs head during collision?

(b) The manufacturer wishes to reduce the average force involved in such a collision to 200 N. In order to acheive this they install a passenger airbag on the front of the glove compartment which quickly inflates in the event of a crash and deflates as the childs head pushes into it, effectively increasing the amount of time it takes to slow the childs head (i.e. the collision lasts longer). How long would the collision between the childs head and the airbag need to last to reduce the speed of the head relative to the dashboard from 40 km/h to 0km/h without exceeding the average force quoted above.