Question

HYS 121 - In-Class Problem Graphing with Velocity 4 Below are shown four velocity vs. time graphs. For each: Draw the corresponding position vs. time graph. Assume that the motion takes place along a horizontal Name: line and that xo = 0 m. 4.5 4.5 Time (s) rime (s) 3.5 Time (s) -3 10 T Time (s) 10

Answer 1

For question no. 4 we will use following concepts ( some values have been assumed since they were not clear from the graph but the shape of the graph has been accurately determined.)

1. The v-t graph provides us with dx/dt i.e. slope values of the x-t graph since, v=dx/dt.

2. At points where the velocity is uniformly increasing/decreasing we have used dv/dt= d^{​​​​​​2} x/dt^{​​​​​2} to know the concavity of the x-t graph.

3. Using second equation of motion for the varying velocity graphs we have determined the shape of the x-t graph.

dt at bu OLe 2

For Q5 we draw the x-t graph by the same method above and then confirm the distance values from graph by calculating the area under v-t graph which also gives us the distance.

D) in part b and c the distance comes out to be equal as can also be inferred from the v-t graph. It means that the particle is decelerating and returning back to it's original position (i.e. displacement in the negative direction)