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Date May 2012 Marks available 3 Reference code 12M.2.SL.TZ2.2
Level Standard level Paper Paper 2 Time zone Time zone 2
Command term State Question number 2 Adapted from N/A

Question

This question is about kinematics.

State the difference between average speed and instantaneous speed.

[2]
a.

The graph shows how the acceleration a of a particle varies with time t.

At time t = 0 the instantaneous speed of the particle is zero.

(i) Calculate the instantaneous speed of the particle at t = 7.5 s.

(ii) Using the axes below, sketch a graph to show how the instantaneous speed v of the particle varies with t.

[3]
b.

Markscheme

average speed is the speed over a period of time/distance; instantaneous speed is the speed at a particular instant in time/point in space.

a.

(i) speed=(area under graph =)½×7.5×3;
=10 or 11 or 11.3 (ms-1);

(ii) suitable curve approximating to v=kt2;

b.

Examiners report

As in the previous question, candidates appeared to understand the distinction between average and instantaneous speeds but could not express a concise or (sometimes) meaningful account. Some good answers were seen that used calculus ideas but this was not required by the examiners.

a.

(i) Candidates were required to recognize that the area under an acceleration–time graph yields the speed change of a particle. They were also expected to give a realistic number of significant figures in their answer. This trapped very many.

(ii) A very large majority of candidates were able to give a good sketch of a parabola for their answer. Failing answers included a straight line through the origin and a straight line parallel to the x-axis.

b.

Syllabus sections

Core » Topic 2: Mechanics » 2.1 – Motion
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