Problem 2-99 - v-t graph - Part 10 - (a)

Two cars, A and B, are stopped for a red light beside each other at an intersection. The light turns green and the cars accelerate. Their velocity time graphs are shown in Figure 2 44. (The positive direction is "forward.")

graph indicating car A and car B accelerating

(a) At what time(s) do A and B have the same velocity?
(b) When does B overtake A? (Hint: Their displacements must be equal at that time and displacement can be found from a velocity time graph.)
(c) How far have the cars traveled when B overtakes A?

Accumulated Solution

The velocities are equal at \(\mathrm{t = 45\; s}\)

\(\mathrm{d_{A,60} = (1/2)(15\;m/s)(30\;s) + (15\;m/s)(30\;s) = 675\; m}\)

\(\mathrm{d_{B,60} = (1/2)(20\;m/s)(60\;s) = 600\; m}\)

\(\mathrm{d_{A,60} - d_{B,60} = 75 \;m}\)

\(\mathrm{v_{B,A}= 5\; m/s}\)



In that 15s B travels a further:
\(\mathrm{(15\;s)(20\;m/s) = 300\; m}\)

Total displacement of B (and A) \(\mathrm{= 600\;m + 300\;m = 900\; m = 9.0 \times 10^2\; m}\)