East is to the right and west is to the left. At time t_0, Alice is at the origi

Question

East is to the right and west is to the left. At time t_0, Alice is at the origin, has a velocity of 2.50 m/s to the west and an acceleration 0.300 m/s^2 east. At time t_0, Bob is 50.0 m cast of Alice, and he has a velocity of 0.500 m/s cast and an acceleration 0.120 m/s^2 east. Alice's displacement between time to and time t_1 is equal to Bob's displacement during this same time interval. a. What is the value of t_1? Circle your answer. b. What is Bob's position at time t_1? Circle your answer. To receive full credit, you must show your work. The work must include an appropriate sketch and must use appropriate symbols.

Explanation / Answer

xo = 0

vo = -2.5 m/s

ao = 0.3 m/s2

x1 = 50 m

v1= 0.5 m/s

a1 = 0.12 m/s2

So, displacement of Alice , s = vo*(t1 - to) + 0.5*ao*(t1 - to)^2

So, s = -2.5*(t1 - to) + 0.5*0.3*(t-to)^2 ----------- (1)

and displacment of Bob, s' = 0.5*(t1 - to) + 0.5*(0.12)*(t1- to)^2

Now, s = s'

So, -2.5*(t1 - to) + 0.5*0.3*(t1-to)^2 = 0.5*(t1 - to) + 0.5*(0.12)*(t1- to)^2

So, 3*(t1- to) = 0.5*(0.3 - 0.12)*(t1 - to)^2

So, t1 - to = 3*2/(0.3 - 0.12) = 33.33

So, t1 = ( to + 33.33 ) s

b)

Bob's position = s' = X - 50 = 0.5*(t1 - to) + 0.5*(0.12)*(t1- to)^2

So, X - 50 = 0.5*(33.33) + 0.5*(0.12)*(33.33)^2 = 83.3

So, X = 133.3 m <------ answer

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