The graph shows a museum robot's position. Which of these describes the robot's motion during segment S?
A metro train makes a run you could describe over the radio. Stage 1: it holds 8 m/s for 3 s. Stage 2: it slows steadily to rest over the next 2 s. Stage 3: it stands at the platform for 2 s. Stage 4: it sets off in the opposite direction, speeding up steadily to 6 m/s the other way, v = −6 m/s, by t = 10 s. Any trip someone can describe that way, you can draw, stage by stage.
The graph is that radio description, built as a velocity-time graph. Each stage of the description becomes one segment of the graph.
A steady velocity is a flat segment at that velocity's value. The train's first 3 s sit flat at 8 m/s: off the axis, at its level.
At rest is a flat segment ON the time axis, at v = 0. From t = 5 s to 7 s the train's line runs along the axis.
Speeding up at a steady rate is a straight segment heading away from the time axis. Slowing at a steady rate is a straight segment heading toward it. The train's braking stage ramps from 8 m/s down to the axis; its final stage ramps away from the axis.
Motion in the negative direction sits below the time axis. The train's last stage ends at −6 m/s, below the axis.
Construct the velocity-time graph for this ride: a cyclist rides at a steady 4 m/s in the negative direction for 3 s, then slows steadily to rest over 3 s.
Work stage by stage:
stage 1, a steady 4 m/s in the negative direction: a flat segment at −4 m/s, below the axis, from t = 0 to 3 s
stage 2, slowing steadily to rest over 3 s: one straight segment from −4 m/s up to the time axis, reaching v = 0 at t = 6 s
The slowing stage heads toward the axis, and it takes its full 3 s: no vertical jump.
The finished graph: a flat segment at −4 m/s for 3 s, then a straight ramp up to v = 0 at t = 6 s.
A car moves at a steady 5 m/s in the positive direction for 3 s, then slows steadily to rest over 3 s. Panels A to D each show a candidate velocity-time graph. Which panel shows the correct graph?
Construct the velocity-time graph for this run: a cart speeds up steadily from rest to 6 m/s in 2 s, then holds 6 m/s for 4 s.
Work stage by stage:
stage 1, speeding up steadily from rest to 6 m/s in 2 s: one straight segment from the origin up to 6 m/s at t = 2 s, heading away from the axis
stage 2, holding 6 m/s for 4 s: a flat segment at 6 m/s from t = 2 s to 6 s
Holding a speed is flat at its level, not on the axis: a segment on the axis would claim the cart stopped.
The finished graph: a straight ramp from 0 to 6 m/s over 2 s, then a flat segment at 6 m/s until t = 6 s.
Now you draw. On paper, sketch the velocity-time graph for this trip: a go-kart moves at a steady 2 m/s in the positive direction for 4 s, then speeds up steadily to 8 m/s over 2 s, then holds 8 m/s for 2 s. Label the time axis in s and the velocity axis in m/s. When your drawing is done, select Continue to compare it with the model answer.
One more, below the axis this time. On paper, sketch the velocity-time graph for this walk: a dog trots at a steady 3 m/s in the negative direction for 4 s, slows steadily to rest over 2 s, then stays at rest for 2 s. Label both axes, then select Continue to compare.
On paper, sketch the velocity-time graph for this delivery run: a robot moves at a steady 4 m/s in the positive direction for 2 s, slows steadily to rest over 2 s, stays at rest for 2 s, then speeds up steadily in the negative direction, reaching 6 m/s of speed after 3 s, and holds that velocity for 1 s. Label both axes, then select Continue to compare your drawing with the model answer.
A shuttle speeds up steadily from rest to 9 m/s in 3 s, holds 9 m/s for 3 s, then slows steadily to rest in 3 s. Panels A to D each show a candidate velocity-time graph. Which panel shows the correct graph?
A ball rolls in the negative direction, speeding up steadily from rest to a speed of 6 m/s over 3 s, then holds that velocity for 3 s. Panels A to D each show a candidate velocity-time graph. Which panel shows the correct graph?