**Goal:** linking acceleration and velocity graphically.

**Source:** UMPERG

The

plot of velocity versus time is shown at right for three objects. Which

object has the largest acceleration at t = 2.5s?

- Object A only
- Object B only
- Object C only
- Both B and C
- Both A and C
- Both A and B
- All three have the same acceleration at t = 2.5s
- None of the above
- Cannot be determined

## Commentary:

## Answer

(6) Objects (A) and (B) have the same acceleration (i.e., they have the

same slope for the velocity vs. time graph at t=2.5s) Object (C) has a

constant velocity (zero slope).

## Background

After students have been introduced to acceleration, but before they are

given a procedure for determining the acceleration from a graph of

velocity vs. time. Students should answer this question after they have

gained an understanding of the definition of acceleration, but before

they are given any explicit instruction for how acceleration relates to

a velocity vs. time graph.

## Questions to Reveal Student Reasoning

How can you determine if an object is accelerating? For which objects

is the velocity changing. What are some examples of objects moving

according to the graphs?

What features about a velocity vs. time graph indicate that an object

has a zero velocity? Zero acceleration? What features indicate a

negative acceleration? Positive acceleration?

## Suggestions

Redraw the velocity vs. time graph for object (A) twice more. In one

drawing approximate the curve with three straight line segments. In the

second approximate the curve with 6 straight line segments.