First slide

Rectilinear Motion

Question

A particle moving in a straight line covers half the distance with speed of 3 ms^-1. The other half of the distance is covered in two equal time intervals with a speeds of 4.5 ms^-1 and 7.5 ms^-1 respectively. Find the average speed (in m/s) of the particle during this motion

Moderate

Solution

$\begin{array}{l} v_{avg} = \frac{2 v_{0} (v_{1} + v_{2})}{2 v_{0} + v_{1} + v_{2}} \\ \Rightarrow v_{avg} = \frac{2 \times 3 (4 .5 + 7 .5)}{6 + 4 .5 + 7 .5} {ms}^{- 1} \\ \Rightarrow v_{avg} = \frac{6 \times 12}{18} {ms}^{- 1} = 4 {ms}^{- 1} \end{array}$

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