1D Kinematics Legacy Problem #13 Guided Solution

There are many ways to describe the motion of objects, from words to diagrams to numbers to equations and finally to graphs, and here what we're doing is describing the motion of Renata Gas using a velocity time-graph. So we're representing over the course of six seconds changes in the velocity of Renata's car, who unfortunately has once more forgotten to fill up her tank. So what I observe is I observe the line sloping downwards indicate the velocity is decreasing, from an initial value of 18 meters per second to a value of zero meters per second at six seconds, and I'm asked two questions. I'm asked to determine the acceleration, and I'm asked to determine the distance. The two things you need to know about velocity time-graphs is that the slope is representative of an object's acceleration, and the area under the line, that is between the line on the graph, and the time axis is representative of the distance traveled by the object. So in this case, in answering A, I'm going to have to calculate a slope, a rise-per-run ratio. That demands that you get two coordinates, for instance, zero seconds and 18 meters per second, and six seconds, zero meters per second, and you do a rise-per-run calculation or a delta y over delta x calculation. So this line rises negative 18 meters per second, meaning it actually falls 18 meters per second, and it runs across six seconds. So I just do that ratio, and I get negative 3.0 meters per second per second. And then to get the area or the displacement or distance of Renata during these six seconds, I have to find the area of a triangle, a triangle being bound on the left side by the velocity axis, on the underside by the time axis, and along the diagonal by the red line. And so that's a one-half base-height calculation for a triangle. I need to go one-half times the base of six seconds times the height of 18 meters per second. So one-half 18 times six will give me a distance.