23. An experiment was carried out to record the velocity of a particle during the first 6 seconds of its journey.
\(v\) is the velocity of the particle measured in m/s.
\(t\) is the time in seconds.
The relationship found was \(v = 6t - t^2\).
(a) Draw a graph of \(v = 6t - t^2\) for values of \(t\) from \(t = 0\) to \(t = 6\). [2]
(b)
(i) Calculate an estimate for the distance the particle travelled from \(t = 0\) to \(t = 6\). You must use six regions, each of equal width, in your calculation. [3]
(ii) Sharmin says,
“The estimate for the distance calculated using six regions of equal width is less than the actual distance travelled by the particle.”
Is Sharmin correct? You must give a reason for your answer. [1]
Mark scheme (a)
Scheme
Marks
Comments
Correct plots for values of \(t\) from 0 to 6 and joined with a curve
B2
B1 for at least 5 correct plots joined with a ‘curve’, or all 7 points plotted accurately but not joined, or not joined with a curve
M1 for at least 4 individual areas correct (2.5 + 6.5 + 8.5 + 8.5 + 6.5 + 2.5) or if 1 slip in the trapezium rule
35 (metres)
A1
CAO
(ii) States or implies Sharmin is correct with a suitable reason, e.g. ‘Correct as all 6 areas are less than the actual areas’, ‘Correct as there are gaps left above the triangles and trapezia’
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