Question

1. this graph shows a trip on a bike trail. the trail has markers every 0.5 km showing the distance from the beginning of the trail.

a. when was the bike rider going the fastest?
b. when was the bike rider going the slowest?
c. during what times was the rider going away from the beginning of the trail?
d. during what times was the rider going back towards the beginning of the trail?
e. during what times did the rider stop?

Explanation:

Step1: Analyze graph slope for speed

Speed = $\frac{\text{Change in Distance}}{\text{Change in Time}}$, steeper slope = faster speed.

Step2: Identify fastest segment

Segment from 2.4 to 3.0 hours has the steepest negative slope (fastest speed, returning).

Step3: Identify slowest segment

Segment from 1.0 to 1.6 hours has the shallowest positive slope (slowest forward speed).

Step4: Identify outward travel times

Distance increases from 0 to 2.4 hours.

Step5: Identify return travel times

Distance decreases from 2.4 to 3.0 hours.

Step6: Identify stopped times

Distance is constant from 1.0 to 1.6 hours.

Answer:

a. Between 2.4 hours and 3.0 hours
b. Between 1.0 hours and 1.6 hours
c. Between 0 hours and 2.4 hours
d. Between 2.4 hours and 3.0 hours
e. Between 1.0 hours and 1.6 hours