Two Toy Cars Are Rolling On Adjacent Straight Tracks

Question

At t = 0, one toy car is set rolling on a straight track with initial position 14.0 cm, initial velocity −3.3 cm/s, and constant acceleration 2.70 cm/s2. At the same moment, another toy car is set rolling on an adjacent track with initial position 9.0 cm, initial velocity 5.10 cm/s, and constant zero acceleration.

(a) At what time, if any, do the two cars have equal speeds? 

(b) What are their speeds at that time?

(c) At what time(s), if any, do the cars pass each other?

(d) What are their locations at that time?

Answer 1

For this kind of problems you need to remember the equations of motion for particles with uniform acceleration.

They give you the functions of position, speed, and acceleration as a function of time and initial conditions.

So to find when are they going to have the same velocity for example, you need to ask for a time T which solves the equation V₁(T)=V₂(T) where V₁(t) and V₂(t) are the functions for the speed of the objects 1 and 2 at a time t.