A car and a truck starts from rest at the same instant, with the car initially at some distant behind the truck. The truck has a constant acceleration of 2.1 m/s^2, and the car at 3.4 m/s^2. The car overtakes the ruck after it has moved 40.0 m.
a) how much time does it take the car to overtake the truck?
b)how far does the car behind the truck initially?
c)what is the speed of each when they abreast?
d)on a single graph, sketch the position of each vehicle as a function of time. take x=0 at the initial location of the truck.
a) Truck --> 40 = x0 + v0t + (1/2)at^2
40 = (1/2)at^2
t = sqrt(80/2.1)
b) Car x = x0 + v0t + (1/2)at^2
x0 = (1/2)(3.4)t^2 - 40
c) Car v = v0 + at --> v = 3.4t
Truck v = v0 + at --> v = 2.1t
d) Plug in values and prosper.