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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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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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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Calculate the total distance travelled by the ball in the first 4 time intervals.
[1 mark]
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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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Show that the velocity increases by a constant amount in each time interval.
[2 marks]
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Calculate the constant difference in velocity between consecutive measurements.
[1 mark]
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Show that if this pattern continues, the velocity at 2.5 seconds would be 6.0 m/s.
[2 marks]
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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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(01.1) Calculate the number of flowers needed for Row 5.
[1 mark]
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(01.2) Calculate the number of flowers needed for Row 10.
[1 mark]
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GCSE Perfect