At t = 0, one toy car is set rolling on a straight track with initial position 1

Question

At t = 0, one toy car is set rolling on a straight track with initial position 13.5 cm, initial velocity -3.4 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 8.0 cm, initial velocity 5.30 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?

Explanation / Answer

(a) Using v = u + at for car A,
5.30 = 3.4 + 2.7 t
then t = 0.704 s (ans)

(b) Both will have the same speed of 5.30 cm/s, BUT
car A is moving to the left at 5.30 cm/s while
car B is moving to the right at 5.30 cm/s. (ans)

(c) They will pass by each other once only.
Initial distance between both cars = 13.5 - 8.0 = 5.5 cm
Car B has a constant velocity of 5.30 cm/s to the right.
Car A's velocity to the left is increasing. Let it be v when both cars met.
Then t = (v - 3.4) / 2.70 [use of t = (v-u)/a]

Relative velocity between the cars = 5.30 - (-v) = (v + 5.3)cm/s
So they will meet at time, t = 5.5 / (v+5.3)

Equating both t equations above, and solving for v.
(v - 3.4) / 2.70 = 5.5 / (v+5.3)

v = 3.245m/s

So they will meet at t = 5.5 / (3.245+5.3)
= 0.644s after they start moving towards each other.

(d) Using car B's constant speed,
car B would have move to the right by 5.30 X0.644
= 3.41 cm.
Since the starting point of car B is at the 8.0cm mark,
so they will meet at the 8.0 + 3.41
= 11.41 cm mark (ans)

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