For each of the following exercises, the goal will be to derive an equation and

Question

For each of the following exercises, the goal will be to derive an equation and answer questions using information obtained from the supplied graphs. Be sure to always indicate the proper units for both the equations and the numerical answers. On a recent space mission a small probe of mass m was sent into an unexplored region of space to investigate an unknown force field. It was hoped that, if the acceleration of the probe could be determined, then Newton's second law, F-ma, would give information about any forces present. The probe was launched with an initial velocity vo at time t0, and its velocity was monitored as a function of time. A partial record of the mission is given below. A. Time (s) 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 Velocity (m/s) 81.4 75.6 69.8 64.0 53.0 524 46.6 40.8 35.0 Use the graph A-1 generated from the above data to answer the following questions. 1. What is the equation that relates the probe velocity to its time of flight? Use the variable names t for time and v for velocity. Any constants in the equation must have the correct numerical values. 0.SD 2. What was the initial velocity of the probe? Did the probe experience any acceleration? If so, what was the value of the acceleration? Give both magnitude and direction (the direction must be given relative to that of the initial velocity). 3. 4. When will the velocity of the probe be zero? 31

Explanation / Answer

1)

By Newton’s 2nd law,

F=ma

a=(vf –v0)/t

vf –v0 = at

v–v0 = at

v=v0 + at

by graph. a=-11.6m/s^2

v=v0 -11.6t

2)

v=v0 -11.6t

at t=1.0s, v=81.4m/s

81.4 = v0 -11.6*1.0

81.4 = v0 -11.6

v0 = 81.4+11.6

v0 = 93.0m/s

3) Yes, the probe experience acceleration

a=(vf –v0)/t

v0 = 93.0m/s,

at t= 1.0s, v=81.4m/s

a=(81.4-93.0)/1.0

a= -11.6m/s^2 ……………..negative sign indicates direction of a is opposite of v0

4)

v=v0 -11.6t

Put v=0m/s, v0 = 93.0m/s

0 = 93.0-11.6*t

Gives, t= 8.02s

At t=8.0s velocity of the probe is zero

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