A skateboarder is moving at 1.75 m/s when she starts going up an incline that causes an acceleration of -0.20 m/s2 How far does she go before she comes to a stop?

Approximately .

Explanation:

The skateboarder started with an initial speed of and came to a stop when her speed became . How much time would that take if her acceleration is ?

.

Refer to the speed-time graph in the diagram attached. This diagram shows the velocity-time plot of this skateboarder between the time she reached the incline and the time when she came to a stop. This plot, along with the vertical speed axis and the horizontal time axis, form a triangle. The area of this triangle should be equal to the distance that the skateboarder travelled while she was moving up this incline until she came to a stop. For this particular question, that area is approximately equal to:

.

In other words, the skateboarder travelled up the slope until she came to a stop.

A more general equation for this kind of motion is:

,

where:

For the skateboarder in this question:

.