A 40 ft truck is traveling down the freeway at 70 fts A car

A 40 ft long truck is traveling down the freeway at 70.0 ft/s (about 48 mph). A car, 10 ft long, has been following this truck, 60 ft behind. The car starts to acc. at 8.0 f/s2 to pass the truck, and the truck driver starts to acc. at 2.0 ft/s?. The car cuts back into the right lane when it is 30 ft ahead of the truck. a) How long does it take? b) Find the final speed of the car and truck. 1o. Initial Final 10 ft 70 ft/s -40ft 4 ft 10 ft 60 ft

Solution

A) the relative acceleration of car-truck = 6ft/s2 and relative velocity = 0

We take the front of truck as origin of coordinate system then

dispalcment required = 110+30=140ft

so

D = ut+0.5*t^2

or

140=0*t+0.5*6*t^2

t = (140/3)^0.5 = 6,83 seconds

b)velcoity of car = u+at = 70+8*6.83= 124.64ft/s

velocity of truck = 70+2*6.83=83.66ft/s