A model train runs on a straight track where east is the positive direction. Its velocity is v = -4 m/s. Which description matches?
A canoeist paddles along a straight channel past a dock. The dock is the origin, and the far side of it counts negative. At 0 s the canoe is 4 m on the negative side, at x = −4 m. It moves steadily in the positive direction, passing the dock at 2 s and reaching +4 m at 4 s. Then it turns and heads back, arriving at the dock again at 8 s.
Where the line sits says which side of the origin the canoe is on. Which way it tilts says which way it is moving. Two different facts.
The tilt is the slope, and the slope of a position-time graph at a moment is the velocity at that moment, sign included. That holds for straight segments and curves alike.
The graph shows a swimmer's position; segment G rises from x = −7 m to x = −1 m. Which way is the swimmer moving during G?
The tilt is what matters: G rises, so its slope is positive.
The negative positions only say the swimmer is on the negative side of the origin.
The swimmer is moving in the positive direction.
The graph shows a metal detectorist's position on a beach. Which way is she moving during segment E?
The graph shows a tour boat's position; the curve through segment H falls while staying above the time axis. Which way is the boat moving during H?
The curve falls: its slope is negative.
Staying above the axis only says the positions are positive.
The boat is moving in the negative direction: a falling curve means motion in the negative direction, even at positive positions.
The graph shows a golf cart's position. Which way is the cart moving during segment D?
The graph shows a courier cyclist's position along a street. Which statement describes her direction of motion during the whole segment shown?
The graph shows a balloon's position. Which way is the balloon moving during segment J?
The graph shows one journey with four labeled segments. During which segment is the object moving in the positive direction?