The line graph shows the position of a particle along the x -axis over time. the letters h to l represent particular moments in time.

1. The graph is of position vs. time, so the instantaneous speed is the slope of the graph. The slope has its largest positive value at point H and its largest negative value at point J. Since the curve at J is steeper than at H, the speed is highest at J. (Speed doesn't care about direction of motion.)

2. time = distance/speed. For the average speed to be 40 mph, the trip must be completed in

... time = (180 mi)/(40 mi/h) = 4.5 h

She has used up

... time = (90 mi)/(30 mi/h) = 3.0 h

of her time, so must complete the last 90 miles in 1.5 hours. Her speed must be

... speed = distance/time = (90 mi)/(1.5 h) = 60 mph

3. The horizontal axis of the graph is minutes, so 60 seconds is located to the left of point A. The slope of the line from the origin to point A is ...

... (5 km)/(15 min) = (1/3) km/min ≈ 0.33 km/min

This is the velocity the problem is asking for.

4. Displacement divided by the time over which it occurred is ...

... average velocity

irrational, cannot