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 east of Alice, and he has a velocity of 0.500 m/s east and an acceleration 0.120 m/s^2 east. Alice's displacement between time t_0 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?
Looking for easy explanation and show of work for each step.

Answer 1

displacement = v0 t + a t^2 / 2

for Alice:

r = -2.50t + 0.30 t^2 /2

r = - 2.50t + 0.15 t^2

For Bob:

r = 0.5t + 0.120t^2 /2

equating both displacements,

- 2.50t + 0.15 t^2 = 0.5t + 0.120t^2 /2

0.09 t^2 - 3t = 0

t (0.09t - 3) = 0

t = 0 Or 33.33 sec

(A) t1 = 33.33 sec

(B) r = xf - xi = 0.5t + 0.120t^2 /2

xf - 50 = 0.5(33.33) + (0.120 x 33.33^2)/2

xf = 133.33 m