Question

trisha is biking to her friends house. she starts off with a burst of speed, but the first half of the trip is on an incline, so she slows down gradually. luckily, the second half of the trip is downhill, so trisha picks up speed again before coasting along steadily. which graph could show trishas speed over time?

Explanation:

Step1: Analyze Initial Speed Change

Trisha starts with a burst (speed increases), then first half (incline) slows gradually (speed decreases). The left graph starts with a non - zero speed, increases, then decreases. The right graph starts with a non - zero speed and decreases first, which doesn't match the initial burst.

Step2: Analyze Second Half Speed Change

Second half is downhill (speed increases) then coasts steadily (speed stabilizes or has a small change). The left graph after decreasing (incline) increases (downhill) and then has a more stable part? Wait, no, re - check. Wait, the right graph: first it decreases (wrong, since she starts with a burst), left graph: starts with a burst (speed up), then slows (incline), then speeds up (downhill) and then maybe stabilizes? Wait, the description: "starts off with a burst of speed (so initial speed increase), but the first half of the trip is on an incline, so she slows down gradually (speed decreases). Luckily, the second half of the trip is downhill, so Trisha picks up speed again (speed increases) before coasting along steadily (speed becomes constant or has a very small change)". The right graph starts with a decrease, which is wrong. The left graph: starts with a speed, increases (burst), then decreases (incline), then increases (downhill) and then maybe a small decrease? Wait, no, maybe I misread. Wait the two graphs: left graph: y - axis speed, x - time. The left graph's curve: starts at some speed, goes up (increase, burst), then peaks, then goes down (slowing on incline), then maybe? Wait no, the second half is downhill, so after the first half (incline) which is slowing, the second half (downhill) should be speeding up. The right graph: starts at a speed, goes down (decrease), then up (increase). But Trisha starts with a burst (increase), so right graph's initial decrease is wrong. So the left graph: initial increase (burst), then decrease (incline), then increase (downhill) and then maybe a small decrease? Wait, maybe the left graph is the one. Wait the problem says "the first half of the trip is on an incline, so she slows down gradually" (so speed decreases after the initial burst), "second half of the trip is downhill, so Trisha picks up speed again before coasting along steadily" (speed increases then stabilizes). The left graph: first increases (burst), then decreases (incline), then increases (downhill) and then maybe a more stable part? The right graph starts with a decrease, which is opposite to the initial burst. So the left graph matches the initial burst (increase), then incline (decrease), then downhill (increase) and then coasting (maybe the end part is more stable? Or maybe the left graph's curve after decreasing (incline) increases (downhill) and then has a small decrease, but the right graph's initial decrease is wrong. So the correct graph is the left one.

Answer:

The graph on the Left