Question

As a traffic light turns green, a waiting car starts with a constant acceleration of 6.0 m/s^2.At the instant the car begins to accelerate, a truck with a constant velcoity of 21 m/s pass in the next lane.

(a) How far will the car travel before it overtakes the truck?
(b) How fast will the car be travelling when it overtakes the truck?

Calculations (a) :

Car:
Vi = 0 m/s
Vf = ?
Acceleration = 6.0 m/s^2

Truck:
Vi = 21 m/s
Vf = 21 m/s
Acceleration = 0 m/s^2


* in order to figure out (a), the deltaD's of both the car and truck must be equal
- i'm not to sure if the deltaT will be the same but it seems as though the intial time is the same

This is all I know so far; I've been trying to sub in equations but nothing seems to work. Could someone please guide me in the right direction. Thanks :)

Answer 1

Write equations for the distance travelled by each car since the instant that the truck passes the car. Set the two distances equal to one another and solve for t. Once you have that, use the equations for the position and velocity of the truck vs time.

Xt = 21 t
Xc = (1/2*6 t^2 = 3 t^2
Xc = Xt when 3t^2 = 21 t
t^2 - 7t = 0
t*(t-7) = 0
t = 0 or 7 s
t=0 is the start time when the truck passes the car; you want the other answer.

Vc = a t = 42 m/s when the car passes the truck