Phy 231
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If the position of a ball rolling along a track changes from 10 cm to 20 cm while the clock time changes from 4 seconds to 9 seconds, what is the average rate of change of its position with respect to clock time during this interval?
Vavg = `ds/`dt = (20cm – 10cm)/(9sec – 4sec) = 10cm/5sec = 2cm/sec
Quantity A is the displacement of the particle while Quantity B is change in clock time during displacement. The net change of A with respect to B is 2cm/sec.
If the velocity of a ball rolling along a track changes from 10 cm / second to 40 cm / second during an interval during which the clock time changes by 3 seconds, then what is the average rate of change of its velocity with respect to clock time during this interval?
`dV = (Vf-V0)/`dt = (40cm/s – 10cm/s)/3s = (30cm/s)/3s = 10 cm/s^2
If the average rate at which position changes with respect to clock time is 5 cm / second, and if the clock time changes by 10 seconds, by how much does the position change?
Vavg = `ds/`dt (5 cm/s) = `ds/(10 s) >rearrange> `ds = 5 cm/s * 10s = 50 cm displacement
You will be expected hereafter to know and apply, in a variety of contexts, the definition given in this question. You need to know this definition word for word. If you try to apply the definition without using all the words it is going to cost you time and it will very likely diminish your performance. Briefly explain how you will ensure that you remember this definition.
The most helpful way of remembering how these values are defined has been the flow diagram of the relationships between velocity, displacement, time, and acceleration.
You are asked in this exercise to apply the definition, and given a general procedure for doing so. Briefly outline the procedure for applying this definition, and briefly explain how you will remember to apply this procedure.
To find rates of change in values with respect to one another, one must identify the values to be assessed and compare them such that Change in A with respect to Change in B, is equivalent to: `dA/`dB.
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five minutes
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