Consider a particle moving along a straight line, whose position as a function of time is given by s(t) = α t² - β t + γ, where α = 1 ms⁻², β = 6 ms⁻¹ and γ = 5 m. The average speed of the particle, in ms⁻¹ from t = 0 to t = 6 s is: (a) 0 (b) 12 (c) 6 (d) 3

Answer: (d). s = t² - 6t + 5, v = 2t - 6 = 0 at t = 3 s, so the particle turns back. s(0) = 5, s(3) = -4, s(6) = 5 m. Distance = |-4 - 5| + |5 - (-4)| = 9 + 9 = 18 m Average speed = 18/6 = 3 m/s, so the answer is (d) 3.

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Distance, Displacement & Average Speed

Consider a particle moving along a straight line, whose position as a function of time is given by $s(t) = \alpha t^2 - \beta t + \gamma$ , where $\alpha = 1\text{ ms}^{-2}, \beta = 6\text{ ms}^{-1}$ and $\gamma = 5\text{ m}$ . The average speed of the particle, in $\text{ms}^{-1}$ from $t = 0$ to $t = 6\text{ s}$ is:

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Answer: (d)

$s = t^2 - 6t + 5$ , $v = 2t - 6 = 0$ at $t = 3$ s, so the particle turns back.
$s(0) = 5$ , $s(3) = -4$ , $s(6) = 5$ m.
Distance $= |{-4} - 5| + |5 - (-4)| = 9 + 9 = 18$ m
Average speed $= \frac{18}{6} = 3$ m/s, so the answer is (d) 3.

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