The velocity versus time graph for a particle going along the X-axis is illustrated in the figure. Calculate the displacement in $0$ to $10 \text{ s}$ in meters.

Question

The velocity versus time graph for a particle going along the X-axis is illustrated in the figure. Calculate the displacement in 0 to 10 s in meters.

Quantrex Academy · Accepted Answer

Correct answer: A. 50

The displacement of a particle is equal to the area under its velocity-time graph.

From the given graph, the area under the curve from

t = 0

to

t = 10 \text{ s}

forms a trapezium with parallel sides

v = 2 \text{ m/s}

and

v = 8 \text{ m/s}

, and height

\Delta t = 10 \text{ s}

.

\text{Displacement} = \text{Area of trapezium}

\text{Displacement} = \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{time interval}

\text{Displacement} = \dfrac{1}{2} \times (2 + 8) \times 10

\text{Displacement} = \dfrac{1}{2} \times 10 \times 10 = 50 \text{ m}

The velocity versus time graph for a particle going along the...