Question

An astronaut has left the space shuttle on a tether to test a new personal maneuvering device. She moves
along a straight line directly away from the shuttle. Her onboard partner measures her velocity before and
after certain maneuvers, and obtains the following results:
A. VL = 0.8 m/s,
B. U 1.6 m/s,
C. U = -0.4 m/s,
U2x = 1.2 m/s; (speeding up)
U2x = 1.2 m/s; (slowing down)
v₂x = -1.0 m/s; (speeding up)
D. U-1.6 m/s,. U2x = -0.8 m/s. (slowing down)
If t₁ = 2 s and t₂ = 4s in each case, find the average acceleration for each set of data.

Answer 1

The average acceleration in case A), B), C), and D) are  0.2 m/s²,  - 0.2 m/s², - 0.3 m/s² and 0.4 m/s² respectively.

A) Initial Velocity V1 = 0.8 m/s

Final Velocity V2 = 1.2 m/s

Time at V1 = t1 = 2 sec

Time at V2 = t2 = 4 sec

Time interval = t = 4 -2 = 2 sec

Average acceleration = Final Velocity - Initial Velocity/ Time Interval

Average acceleration = V2 - V1 / t

Put in the value, we get

a = 1.2 - 0.8 / 2

a = 0.2 m/s²

B) Initial Velocity V1 = 1.6 m/s

Final Velocity V2 = 1.2 m/s

Time at V1 = t1 = 2 sec

Time at V2 = t2 = 4 sec

Time interval = t = 4 -2 = 2 sec

Average acceleration = Final Velocity - Initial Velocity/ Time Interval

Average acceleration = V2 - V1 / t

Put in the value, we get

a = 1.6 - 1.2 / 2

a = - 0.2 m/s²

C) Initial Velocity V1 = - 0.4 m/s

Final Velocity V2 = -1 m/s

Time at V1 = t1 = 2 sec

Time at V2 = t2 = 4 sec

Time interval = t = 4 -2 = 2 sec

Average acceleration = Final Velocity - Initial Velocity/ Time Interval

Average acceleration = V2 - V1 / t

Put in the value, we get

a = -1 - (-0.4)/ 2

a = - 0.3 m/s²

D) Initial Velocity V1 = -1.6 m/s

Final Velocity V2 = -0.8 m/s

Time at V1 = t1 = 2 sec

Time at V2 = t2 = 4 sec

Time interval = t = 4 -2 = 2 sec

Average acceleration = Final Velocity - Initial Velocity/ Time Interval

Average acceleration = V2 - V1 / t

Put in the value, we get

a =  -0.8 - (-1.6) / 2

a = 0.4 m/s²

Therefore, average acceleration in case A), B), C), and D) are  0.2 m/s²,  - 0.2 m/s², - 0.3 m/s² and 0.4 m/s² respectively.

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