Question

Answer 1

In a velocity vs. time graph, the area underneath the graph isthe change in position. You can quickly calculate the area bybreaking the graph into multiple triangles and rectangles andsumming the results.

1. 0 < t < 2

0.5 * 2s * 9m/s = 9m

2 < t < 6

0.5 * 4s * (9-5)m/s + 4s * 5 m/s = 8m + 20m = 28m

Δx at 6 seconds then is 37m

x_final = 10m + 37m = 47m

2. 6 < t < 8

This one is a little trickier, but you know that the slope is-1/3, so in 2 seconds the velocity is -2/3.

0.5 * 2s * -2/3 m/s + 2s * -1/3 m/s = -2/3 - 2/3 = -4/3m

Δx at 8 seconds is 37m - 4/3m = 35.67m

x_final = 10m + 35.67 = 45.67m