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The position of a rabbit along a straight tunnel as a function of time is plotted. what is its instantaneous velocity

User Anomie
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Since the plot is not given, I;m not sure I can give the exact answer since there are two possible cases. If the plot is linear, then the instantaneous velocity is the same for each point in the plot. This is equal to the slope of the line. However, if the plot is a curve, you have to be specific at what time you would like to determine the instantaneous velocity. The slope at that point would be the instantaneous velocity of the motion. For example, the equation of the curve is:

x = t² + 5t + 3
If you want to find the inst. velocity at t = 2s, differentiate the equation and replace t with 2:
dx/dt = 2t + 5 = 2(2) + 5 = 9 m/s
User Lukas Thaler
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