Question

An automobile and a truck start from rest at the same instant,with the automobile initially at some distance behind the truck.The truck has a constant acceleration of 2.20m/s2,and the automobile has an acceleration of 3.50m/s2.The automobile overtakes the truck after truck has moved 60.0m.
a)How much time does it take the automobile to overtake the truck?
b)How far the automobile behind the truck initially?
c)What is the velocity of each when they are next to each other?.

Answer 1

a)How much time does it take the automobile to overtake the truck?
After t
seconds, the truck moved:
60.0 = 0.5*2.20 * t^2, so t = sqrt(2*60.0 / 2.20) =
approx. 7.385 s.

b)How far the automobile behind the truck
initially?
Let that distance was n meters.
When they met, automobile
moved:
60.0 + n = 3.50 * t^2 = 3.50 * 27.2727 = 95.4545 m, so
n = 95.4545 - 60.0 = 35.45 m.

c)What is the velocity of each when they are next to
each other?.
Truck: Vt = at * t = 2.20 * 7.385 = 16.25 m/s.
Automobile:
Va = aa * t = 3.50 * 7.385 = 25.85 m/s.