course PHY 231
6/30 23:16
Assignment 2 - Problem 1If the velocity of the object changes from 5 cm / sec to 14 cm / sec in 9 seconds, then at what average rate is the velocity changing?
&&&& 'dv_avg = 14cm/sec - 5cm/sec = 9cm/sec
that would be just v_Ave; `d indicates the Delta symbol, indicating 'change in'.
&&&& 'dt = 9sec
&&&& rate_avg = change in A / change in B
&&&& rate_V_avg = 'dv_avg / 'dt = (9cm/sec) * (1/9sec) = 1cm/sec^2
This question asks for rate of change of velocity, `dv, not `dv_Ave (which as noted above isn't a well defined quantity). v_Ave for this interval doesn't change, so it doesn't make sense to talk about the change in vAve.
That is, the A quantity is not v_Ave. The A quantity for the requested rate is velocity, so change in A is change in velocity.
It requires 5.1 seconds, starting from rest, for a ball to roll the 38 centimeter length of a uniform incline.
What is its average velocity?
An object which accelerates uniformly from rest will attain a final velocity which is double its average velocity.
&&&& 'dx = 38cm
&&&& 'dt = 5.1sec
&&&& V_avg = 38cm/5.1sec = 7.45cm/sec ~~ 7.5cm/sec
What therefore is the final velocity of this ball?
What average rate is the velocity of the ball therefore changing?
At what average rate does the velocity of an airplane change, if it accelerates uniformly down a runway, starting from rest, requiring 10 seconds to cover a distance of 154 meters.
&&&& Since V_avg = (V_i + V_f) / 2 then you can multiply the average by two, and we already know that V_i = 0, so the answer is:
&&&& v_f = 2*V_avg = 2*7.5cm/sec = 15cm/sec final velocity
You have found vAve and vf, but you haven't yet found the rate of change of velocity with respect to clock time.
&&&& V_avg = 154m/10sec = 15.4m/sec and V_i = 0
&&&& V_f = 2*V_avg = 2*15.4m/sec = 30.8m/sec
Again you have found vAve and vf, but you haven't yet found the rate of change of velocity with respect to clock time.
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