Two carts roll on the same straight track. Cart A has v = +5 m/s and cart B has v = -5 m/s. What do the two velocities share, and how do they differ?
A remote-control car rolls forward at 2 m/s. Then its driver squeezes the trigger: by t = 2 s the car is doing 8 m/s, its fastest of the run. After that it slows, and somewhere along the way it starts rolling backward, because by t = 9 s it is moving at 6 m/s in the negative direction, v = −6 m/s. At exactly what moment did the car turn around?
One read carries this whole lesson, and you've already made it: above the time axis the velocity is positive; below it, negative. Up to some moment the car's line sits above the axis, so the car moves forward. After that moment the line sits below, so the car moves backward.
The car's line crosses the axis at t = 6 s, so the car turns around at t = 6 s. Not at the peak. At t = 2 s the car is at its fastest, 8 m/s, and still moving forward. A peak is where the speed tops out, not where the direction flips.
The graph shows a truck's velocity. At what time does the truck reverse direction?
The line crosses the time axis at t = 5 s: positive before, negative after.
A change of sign is a change of direction, so the reversal happens there.
The truck reverses direction at t = 5 s.
The graph shows a cart's velocity. At what time does the cart reverse direction?
The graph shows a runner's velocity, which peaks at t = 3 s. Does the runner reverse direction at t = 3 s?
At t = 3 s the velocity is 9 m/s: still positive, so the runner is still moving in the positive direction.
After the peak the runner slows, but the line never crosses the time axis, so the sign never changes.
No. The runner slows after t = 3 s but never reverses: the line never crosses the axis.
The graph shows a van's velocity. At what time, if any, does the van reverse direction?
The graph shows a rover's velocity. At what time does the rover reverse direction?
The graph shows a patrol drone's velocity over 8 s. At which times does the drone reverse direction?
The graph shows a lift platform's velocity: it falls to exactly zero at t = 4 s, touching the time axis, then rises again without going below it. Does the platform reverse direction at t = 4 s?
The graph shows a different car's velocity, crossing the time axis at t = 6 s. Which statement describes the car's motion?