At t =0 one toy car is set rolling on a straight track with intial position 17.0 cm , intial velocity -3 cm/s, and constant acceleration 2.30 cm/s^2 . at the same moment , another toy car is set rolling on an adjacent track with initial position 9.5 cm , intial velocity 5.0 cm/s, and constant zero acceleration. (a) at the 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 location at that time?

a) 5.65 s

b) 5cm/s

c) They will pass each other at both 1.1168 s and 5.84s

d)15.084cm and 38.7 cm

Explanation:

For part A, you need to keep in mind that acceleration is the rate of change of velocity per unit of time. For a constant acceleration, this can be told in this way:

Reordering this equation, we can get v in terms of the initial velocity, the acceleration, and the time elapsed:

Now, we can get the expressions for velocity of each toy car, and equalize them:

As toy car has no acceleration and, therefore, constant speed, both car will have the same speed when toy car 1 reaches this velocity = 5cm/s

c) The position of car 1, as it follows a constant acceleration motion, is given by this equation:

The position for car 2, as it has constant velocity, is given by this equation:

We equalize both equation to find the time where the cars pass each other:

The car will pass each other at both 1.1168s and 5.84s.

For the positions, we solve any of the position equation with the solutions:

the amount of current in the coil

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y