First slide

Rectilinear Motion

Question

If a particle is moving on a straight line, then its velocity time graph is sinusoidal as shown in the figure.
The distance (in m) travelled by the particle in 2 s is _______.

Moderate

Solution

$∵ v = a \sin ω t$
$\begin{array}{l} Or v = π \sin \frac{2 π}{2} t \\ Or v = π \sin π t \end{array}$
The speed-time graph is
$\begin{array}{l} ∵ Speed = | v | \\ ∴ Distance = \int_{0}^{2} | v | d t = 2 \int_{0}^{1} | v | d t \\ = \frac{2 π}{π} [- \cos π t]_{0}^{1} = \frac{2 π}{π} \times 2 = 4 m \end{array}$

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