Question

At t = 0, one toy car is set rolling on a straight track with initial position 16.0 cm, initial velocity -3.9 cm/s, and constant acceleration 3.00 cm/s2. At the same moment, another toy car is set rolling on an adjacent track with initial position 10.5 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.) 3.17 s

(b) What are their speeds at that time? ) 5.6 cm/s

(c) 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.)

(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 cm

Answer 1

xi1 = 16.0cm , vi1=-3.9cm/s , a1=3.00cm/s^2,

xi2 = 10.5cm, vi2=5.60cm/s , a2=0m/s^2

a) Here

a1 = (vf1-vi1)/t

3.00=(vf1+3.9)/t

vf1 = 3.00t - 3.9 ----------------(1)

A2 = (vf2-vi2)/t

0 =(vf2 - 5.6)/t

vf2 = 5.6cm/s ---------------(2)

Since vf1=vf2

vf1 = 5.6cm/s -------------(3)

Plugging (3) in (1)

5.6= 3.00t - 3.9    => 3.17s

b)  From (2) and (3)

vf2=vf1 = 5.6cm/s

c)

Use equation

xf = xi + vi*t +1/2*at^2

For car1 ,

xf1 = xi1 + vi1*t1 +1/2*a1*t1^2

xf1 = 16.0  -3.9*t1 +1/2*3.0*t1^2 ----------------(4)

For car2 ,

xf2 = xi2 + vi2*t2 +1/2*a2*t1^2

xf2 = 10.5 + 5.6*t2 +1/2*0*t1^2

xf2 = 10.5 + 5.6*t2----------------(5)

When cars pass each other ,

xf2 = xf1 and t1=t2=t(say)

Equating (4) and (5)

16.0  -3.9*t +1/2*3.0*t^2 = 10.5 + 5.6*t

Thus t = 0.64s and t = 5.7s

d)

For t= t = 0.64s

xf1=xf2 = 16.0  -3.9*t1 +1/2*3.0*t1^2 = 16.0  -3.9*0.64 +1/2*3.0*0.64^2 = 14.12cm

For t= t = 5.7s

xf1=xf2 = 16.0  -3.9*t1 +1/2*3.0*t1^2 = 16.0  -3.9*5.7 +1/2*3.0*5.7^2 = 42.5cm