Stage 9 - Q1 - 3 marks
Find the speed during the first four seconds.
Hint
Use endpoints of the first segment.
Stage 9 - Q2 - 3 marks
Find the speed from 7 s to 12 s.
Hint
Subtract both endpoint coordinates.
Stage 9 - Q3 - 3 marks
Compare the two speeds and state the difference.
Hint
On shared axes the steeper distance-time line has greater speed.
Stage 9 - Q4 - 4 marks
Tank A falls from 120 cm to 40 cm in 20 min. B falls from 100 cm to 50 cm in 10 min. Compare the rates of depth decrease.
Hint
Visual steepness on different scales is not a rate comparison.
Stage 9 - Q5 - 4 marks
The graph shows distance from home. Find total distance travelled and the speed on the return.
Hint
A zero final distance from home does not mean zero distance travelled.
Stage 9 - Q6 - 4 marks
Runner A starts at \(t=0\) at 5 m/s. B starts from the same place 4 s later at 7 m/s. When does B catch A, measured from A’s start?
Hint
Use one clock but different running durations.
Stage 9 - Q7 - 3 marks
Two depth-time graphs for tanks numbered 3 and 8 look equally steep but use different scales. Must depth fall at the same rate?
Hint
Rate is a ratio of coordinate changes, not a page angle.
Stage 9 - Q8 - 4 marks
A vehicle travels at 4 m/s for 3 s and 8 m/s for 9 s. Find the overall average speed and explain why the simple mean is wrong.
Hint
Weight each speed by the time spent at that speed.
Stage 9 - Q9 - 4 marks
A trip covers 140 m in 10 s. The first 4 s are at 7 m/s; the rest is at one constant speed. Find the second speed.
Hint
Total time and total distance must each be split consistently.
Stage 9 - Q10 - 5 marks
Challenge: A traveller covers 180 m at a constant moving speed of 6 m/s, with one rest. The overall average speed is \(\frac{9}{2}\) m/s. Find the rest duration and explain why it is positive.
Hint
The slower overall rate includes time with no added distance.