, one toy car is set toy car is set rolling on an adjacent track with initial po

Question

, one toy car is set toy car is set rolling on an adjacent track with initial position 12.0 cm, initial velocity 6.5o cm/s, and constant zero acceleration. (a) At what time, if any, do the 2.50 two cars have equal speeds? (Enter NA if the cars never have equal speeds cm/s blank. I there are two times, enter the smaller time first. If (c) At what time(s), if any, do the cars pass each other? (If there is only one time, enter NA in the they never pass, enter NA in both blanks) (d) What are their locations at that time? (If there is only one position, enter NA in the second biank. i never pass, enter NA in both blanks.) If there are two positions, enter the smaller position first. If they

Explanation / Answer

a]

for the first toy car, |v| = 2.7 + 2.5t

for the second toy car, |v| = 6.5 cm/s

so, 6.5 = 2.7 + 2.5t

=> t = 1.52s.

this is the time when both have equal speeds.

b] their speeds at this time are, v1 = 6.5cm/s and v2 = 6.5 cm/s.

c] for the first toy, the position is given by:

x = 14 - 2.7t - (1/2)2.5t2

=> x = 14 - 2.7t - 1.25t2

for the second toy,

x = 12 + 6.5t

equating the two distances gives,

12 + 6.5t = 14 - 2.7t - 1.25t2

1.25t2 + 9.2t - 2 = 0

this gives only one positive root which is t = 0.211s

so, t1 = 0.211s and t2 = NA.

this is the time when they cross each other.

d] At this time, their locations are:

x = 12 + 6.5(0.211) = 13.3715 cm.

e] (a) asks if they ever attain same speeds while (c) asks if they ever cross each other, meaning if they have a same location at any instant in time.

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