Question

1- What physical quantity is represented by the slope of a Position vs. Time plot? What are its dimensions? How did you know? Please explain.

2- What physical quantity is represented by the slope of a Velocity vs. Time plot? What are its dimensions? How did you figure it out? Please explain.
3- What would the Acceleration vs. Time plot look like for an object moving at constant velocity? Try drawing it and uploading a picture of your graph.

Answer 1

1.

slope of position- time graph= displacement / time = velocity

v = displacement / time = meter/ second

dimension = [ L T ^ - 1 ]

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2.

slope of v-t curve = velocity difference / time = acceleration

a =(m/s) /s = m/s^2

dimension = [ LT^-2]

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3.

if the velocity is constant then Acceleration must be zero.

graph shows as below

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do comment in case any doubt will reply for sure.. Goodluck