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 -4.1 cm/s, and constant acceleration 2.20 cm/s2. At the same moment, another toy car is set rolling on an adjacent track with initial position 11.5 cm, initial velocity 4.50 cm/s, and constant zero acceleration.

a) At what time(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.)
  
   s
. s

b) 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.)
  
Enter a number. cm
  
Enter a number. cm

Explanation / Answer

Given,

t = 0 ; x1 = 13.5 cm ; v1 = -4.1 cm/s ; a1 = 2.2 cm/s^2 ; x2 = 11.5 cm ; v2 = 4.5 cm/s ; a' = 0

a)S = ut + 1/2 at^2

x1' = 13.5 - 4.1 t + 2.2 t^2

x2' = 11.5 + 5.5 t + 0

they would pass each other when x1 = x2

13.5 - 4.1 t + 2.2 t^2 = 11.5 + 5.5 t

2.2 t^2 - 9.6 t + 2 = 0

t = 4.14s ; 0.22 s

b)x1' = 13.5 - 4.1 x 0.22 + 2.2 x 0.22^2 = 12.7 cm

x2' = 11.5 + 5.5 x 4.14 = 34.27

Hence, 12.7 cm and 34.27 cm

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