Question

Please answer fully, thank you!

At t 0, one toy car is set rolling on a straight track with initial position 14.5 cm, initial velocity -4.2 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 9.5 cm, initial velocity 5.60 cm/s, and constant zero acceleration. (a) At what time, if any, do the two cars have equal speeds? (Enter NA If the cars never have equal speeds.] (b) What are their speeds at that time? (Enter NA if the cars never have equal speeds.) cm/s (c) At what tlme(s), If any, do the cars pass each other? (If there is only one time, enter NA In the second blank. If there are two times, enter the smaller time first. If 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 blank. If there are two positions, enter the smaller position first. If they never pass, enter NA in both blanks.) cm (e) Explain the difference hetween question (a) and question (c) as clearly as possible

Answer 1

(a) as the second car has constant speed

we have

-4.2 + 2.70t = 5.60

t = 3.629 sec

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(b) both will have same speed

5.60 cm/s

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(c) equation for positions is given a

x1 = 14.5 - 4.2t + 1.35*t²

x2 = 9.5 + 5.6t

set x1 = x2

14.5 - 4.2t + 1.35*t² = 9.5 + 5.6t

1.35t² - 9.8t + 5 = 0

solve for t

we get

t = 9.8 +/- 8.31 / 2.7

t = 6.71 sec and t = 0.5518 sec

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(d) locations where they pass one another

we get

x1 = 9.5 + 5.6t = 12.6 cm

x2 = 9.5 + 5.6t = 47.1 cm