Question

Figure 2-17 gives the acceleration a(t) of a Chihuahua as it chases a German shepherd along an axis. In which of the time periods indicated does the Chihuahua move at constant speed?

Short answer

Chihuahua moves with constant speed during the time period E

Step-by-step solution

Given information

The graph is shown in figure 2.17

To understand the concept of acceleration

The concept used to solve this problem is constant speed and acceleration. The acceleration is the rate of change of velocity. Acceleration is a vector quantity. If speed is constant and its direction is not changing then there will be no acceleration.

To find the time period in which the Chihuahua moves at a constant speed

The acceleration can be written as,

$\overrightarrow{a}=\frac{d\overrightarrow{v}}{dt}$

Therefore, if$\overrightarrow{a}=0$

$\frac{d\overrightarrow{v}}{dt}=0$

This implies that the velocity is constant.

It means that to find out the time period that has a constant speed, we need to find the time period that has zero acceleration. From the given graph it can be seen that only time period E has zero acceleration. For all the other time periods, the acceleration is increasing, decreasing, positive or negative.

Thus, it can be concluded that Chihuahua moves with constant speed during the time period E.