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At t = 0, one toy car is set rolling on a straight track with initial position 13.5 cm, initial velocity -4.2 cm/s, and constant acceleration 2.60 cm/s2. At the same moment, another toy car is set rolling on an adjacent track with initial position 8.5 cm, initial velocity 5.20 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? ...?

Answer :

(a) We must first look at the formulas of the velocities of each toy car. v1 =
-4.2 + 2.60t. v2 = 5.20. When the two cars have equal speed, then 
v1 = v2
-4.2 + 2.60t = 5.20
2.60t = 9.40
t = 3.62 s

(b) Their speed would then be 5.20 m/s. The toy car does not change speed since it doest not have any acceleration.
(c) The two cars will pass each other when their positions are equal.
x1 = 13.5 - 4.2t + 0.5*2.60t^2
x2 = 8.5 + 5.20t
x1 = x2
13.5 - 4.2t + 1.30t^2 = 8.5 + 5.20t
1.30t^2 - 9.40t + 5.0 = 0
t = 6.65s or t = 0.58 s

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