CAIE A-Level Physics 2.1.3 Displacement from Velocity–Time Area

Practise finding signed displacement from areas under velocity-time graphs, combining positive and negative regions and reporting direction, units and interval.

Exam points

Determine displacement from the signed area under a velocity–time graph.
Split a velocity–time graph into appropriate geometric regions and combine positive and negative areas.
Interpret the displacement with direction, units and the stated time interval.

[Maximum number: 2]

The string is now used to move the cylinder in (a) vertically upwards through the water. The variation with time t of the velocity v of the cylinder is shown in Fig. 2.2.

Fig. 2.2

The top face of the cylinder is at a depth of 0.32 m below the surface of the water at time t=0.

Use Fig. 2.2 to determine the depth of the top face below the surface of the water at time $t=4.0 \mathrm{~s}$ .
depth = m

$\begin{aligned} \text { distance } =(1 / 2 \times 2.5 \times 0.10)+(1 / 2 \times 1.5 \times 0.10) \text { or }(1 / 2 \times 4.0 \times 0.10) =0.20(\mathrm{~m})) \end{aligned}$

C1

$\begin{aligned} \text { depth } =0.32-0.20 =0.12 \mathrm{~m} \end{aligned}$

A1

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2.1.3—Displacement from the area under a velocity–time graph question 1