# When are the speed and velocity of this object increasing?

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Shown is a graph of v versus t, the velocity of an object over time.

1)On which of the five sections marked is

the speed of the object increasing?

2)On which of the five sections marked is

the velocity of the object increasing?

Shown is a graph of v versus t, the velocity of an object over time.

1)On which of the five sections marked is

the speed of the object increasing?

2)On which of the five sections marked is

the velocity of the object increasing?

##### 2 Answers

#### Answer:

Sections A, C, and E

#### Explanation:

Speed increases when velocity and acceleration have the same sign. In section A, the velocity is positive because it's above the x axis and the slope is positive, meaning that the acceleration is positive.

In section B, the velocity is positive, but the slope is negative, so they have different signs and therefore the speed is decreasing.

In section C, the velocity is negative and the slope is negative, meaning that the speed is increasing.

Section D, negative velocity, positive slope, so decreasing speed.

Section E, both velocity and slope are positive again

#### Answer:

1) Speed is increasing in sections A, C, and E.

2) Velocity is increasing in sections A, and E.

#### Explanation:

1) Speed is never negative -- it is the magnitude (can also be described as absolute value) of velocity. So speed is distance on the graph from the x axis (time axis), in either direction. Notice in section A that it starts fairly close to the x axis (low speed) and increases (changing to higher speed) the distance from the x axis as time increases. Therefore speed is increasing in section A.

Speed is increasing in sections A, C, and E.

2) Velocity is negative when it is below the x axis.

Velocity is increasing in sections A, and E.

There may be different opinions about whether to say velocity is increasing in a case like section D. Velocity in section D is negative but is changing to be less negative -- heading toward the positive velocity territory. I say that is not an increase, but some might consider that since it is a velocity change in the positive direction it is therefore an increase. You might want to consider what has been said in class about that conflict.

I hope this helps,

Steve