Calculate — 5 marks
A student investigates the motion of a ball rolling down a ramp. The ball starts from rest and travels increasing distances in successive equal time intervals of 0.5 seconds. The distances travelled in each interval are: 0.1 m, 0.3 m, 0.5 m, and 0.7 m.
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(a) Calculate the average velocity of the ball during the second time interval (0.5 s to 1.0 s).
[2 marks]
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(b) The distances form an arithmetic sequence. Calculate the common difference and predict the distance that would be travelled in the fifth time interval.
[2 marks]
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(c) Calculate the total distance travelled by the ball in the first 4 time intervals.
[1 mark]
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- (a) Average velocity = distance ÷ time (1 mark)
- (a) Average velocity = 0.3 ÷ 0.5 = 0.6 m/s (1 mark)
- (b) Common difference = 0.3 − 0.1 = 0.2 m (or equivalent calculation) (1 mark)
- (b) Fifth interval distance = 0.7 + 0.2 = 0.9 m (1 mark)
- (c) Total distance = 0.1 + 0.3 + 0.5 + 0.7 = 1.6 m (1 mark)
Show — 5 marks
A student is investigating the motion of a ball rolling down a ramp. She releases the ball from rest and measures its velocity at regular 0.5 second intervals. The results are shown in the table below.
Time (s): 0, 0.5, 1.0, 1.5, 2.0
Velocity (m/s): 0, 1.2, 2.4, 3.6, 4.8
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(a) Show that the velocity increases by a constant amount in each time interval.
[2 marks]
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(b) Calculate the constant difference in velocity between consecutive measurements.
[1 mark]
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(c) Show that if this pattern continues, the velocity at 2.5 seconds would be 6.0 m/s.
[2 marks]
Show mark scheme
- (a) Identifies the differences between consecutive velocities (1.2 m/s, 1.2 m/s, 1.2 m/s, 1.2 m/s) - 1 mark
- (a) States that all differences are equal / constant - 1 mark
- (b) Calculates 1.2 m/s (or equivalent from any pair of consecutive values) - 1 mark
- (c) Adds the constant difference to the velocity at 2.0 s: 4.8 + 1.2 = 6.0 m/s - 1 mark
- (c) Correctly identifies this as following the arithmetic sequence pattern - 1 mark
Calculate — 2 marks
A florist is creating a display with rows of flowers. The number of flowers in each row follows a sequence pattern. Row 1 has 4 flowers, Row 2 has 7 flowers, Row 3 has 10 flowers, and Row 4 has 13 flowers.
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(a) Calculate the number of flowers needed for Row 5.
[1 mark]
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(b) Calculate the number of flowers needed for Row 10.
[1 mark]
Show mark scheme
GCSE Perfect