Question

The graph shows the distance a ball has traveled x seconds after it was thrown. What is the average speed between 2 seconds and 8 seconds.

Answer 1

The average speed between 2 seconds and 8 seconds is
`0.5ms^(-1)`

Explanation:

It is given that the graph shows the distance a ball has traveled x seconds after it was thrown.

Since, we know that Average speed=
`(Total distance travelled)/(Total time taken)`.

Since the graph represents change is distance with respect to change in time, so we can find average speed of ball by finding the slope of our function using points (2,3) and (8,6). Thus, the slope is given as:

Slope=
`(y_(2)-y_(1))/(x_(2)-x_(1))`

=
`(6-3)/(8-2)`

=
`(3)/(6)`

=
`(1)/(2)`

=
`0.5ms^(-1)`

Therefore, the average speed between 2 seconds and 8 seconds is
`0.5ms^(-1)`.

Answer 2

0.5 meters per second.

Explanation:

We have been given a graph that represents the distance a ball has traveled x seconds after it was thrown.

We can see from our graph that x is independent variable and distance traveled is dependent variable.

We know that
`\text{Average speed}=\frac{\text{Total distance traveled}}{\text{Total time taken to travel the distance}}`

Since the graph represents change is distance with respect to change in time, so we can find average speed of ball by finding the slope of our function using points (2,3) and (8,6).

`\text{Slope}=(y_2-y_1)/(x_2-x_1)`, where,

`y_2-y_1` = Change in two y-coordinates,

`x_2-x_1` = Change in same x-coordinates of two y-coordinates.

Upon using coordinates of our given points we will get,

`\text{Slope}=(6-3)/(8-2)`

`\text{Slope}=(3)/(6)`

`\text{Slope}=0.5`

Therefore, the average speed of ball between 2 seconds to 8 seconds is 0.5 meters per second.