Motion

A runner completes one 400 m lap and stops at the starting line after 80 s. Which statement is correct?

1. A

   Distance = 0 m and displacement = 400 m

2. B

   Distance = 400 m and displacement = 0 m

3. C

   Distance = 400 m and displacement = 400 m

4. D

   Distance = 5 m and displacement = 0 m

1. a

   Select and explain Select the correct statement and explain the difference between the two quantities in this journey.

   3
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   Correct choiceB

   1. 1

      Selects option B: distance = 400 m and displacement = 0 m.

   2. 2

      Explains that distance is the total path length, so it is 400 m.

   3. 3

      Explains that displacement depends only on the change in position, which is zero because the runner returns to the start.

A delivery robot moves in a straight corridor. Its position is measured from a fixed doorway.

1. a

   Calculate Calculate the robot's velocity from 0 s to 4 s.

   2
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   1. 1

      Uses velocity = change in position ÷ change in time.

   2. 2

      Obtains (6 − 0) ÷ 4 = +1.5 m s⁻¹.

2. b

   Interpret Describe the motion from 4 s to 8 s, including direction.

   3
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   1. 1

      States that the robot is stationary from 4 s to 6 s because its position is unchanged.

   2. 2

      States that it then moves back toward the doorway from 6 s to 8 s.

   3. 3

      Calculates or states the return velocity as (2 − 6) ÷ 2 = −2.0 m s⁻¹.

3. c

   Compare Compare the robot's speed before and after the stop.

   2
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   1. 1

      Compares magnitudes 1.5 m s⁻¹ and 2.0 m s⁻¹.

   2. 2

      Concludes that the robot moves faster after the stop, by 0.5 m s⁻¹.

A designer aims a fountain nozzle horizontally from a platform 1.25 m above a pool. Water leaves at 4.0 m s⁻¹. A simple projectile model uses g = 10 m s⁻² and ignores air resistance. The target drain is 2.2 m horizontally from the nozzle.

1. a

   Determine Determine the modelled time for the water to fall to pool level.

   2
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   1. 1

      Uses 1.25 = ½ × 10 × t².

   2. 2

      Obtains t = 0.50 s.

2. b

   Predict Predict whether the water reaches the drain and support the prediction quantitatively.

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   1. 1

      Calculates horizontal distance = 4.0 × 0.50 = 2.0 m.

   2. 2

      Concludes that the model predicts the water lands 0.2 m short of the 2.2 m drain.

3. c

   Evaluate Evaluate how useful this result is for the real fountain and recommend one next design step.

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   1. 1

      Identifies a relevant model limitation, such as water breaking into droplets, air drag, or an uncertain exit speed.

   2. 2

      Explains a likely effect of that limitation or uncertainty on the landing position.

   3. 3

      Recognises that a 0.2 m shortfall is large enough that relying on the ideal result alone is risky.

   4. 4

      Recommends a controlled prototype test or adjustable nozzle followed by measured landing positions.