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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# a) Explain how you can use the graph of position versus time in Figure 2.54 to describe the change in velocity over time. Identify (b) the time ( ta, tb , tc , td , or te ) at which the instantaneous velocity is greatest, (c) the time at which it is zero, and (d) the time at which it is negative. Figure 2.54

a) In the distance versus time graph, velocity is determined by the slope of the graph.

b) At time ta, the instantaneous velocity is maximum.

c) The time at velocity is zero is td.

d) The time at which velocity is decreasing is te

See the step by step solution

## Step 1: Determine the velocity using slope

The velocity is the ratio of the displacement traveled to the time taken to travel that displacement.

If we draw a graph of displacement and time, we get a curve,

At any point, if we take the slope of the graph, it will give the value of velocity.

(a) Here, we can see that at point a, the slope of tangent to point a is maximum.

Hence it can be said that the value of velocity is maximum at A.

As we go from a to b, the slope value decreases continuously.

Hence by watching the slope of the graph, it can be said that whether the velocity will increase or decrease.

Slop is decreasing

So if we plot a graph of velocity versus time, we can answer the remaining questions.

V = slope

V = tan$\mathbf{\theta }$

In addition, the tangent's angle on the graph is dropping. As a result, the slope will decrease. It indicates that the particle's velocity is decreasing.

## Step 2: Velocity versus time graph

Velocity versus time graph

b) It can be seen from the accompanying graph of instantaneous velocity vs. time that the velocity is maximum at ta.

c) It can be seen from the preceding graph of instantaneous velocity vs. time that the velocity is 0 at the td.

d) It can be seen from the preceding graph of instantaneous velocity vs. time that the velocity is negative at that te.