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

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Correct answer: D. 3

Given s(t) = t^2 - 6t + 5 Velocity v(t) = ds dt = 2t - 6 The particle comes to rest when v(t) = 0, which gives t = 3 s. Position at t = 0 s is s(0) = 5 m. Position at t = 3 s is s(3) = 3^2 - 6(3) + 5 = -4 m. Position at t = 6 s is s(6) = 6^2 - 6(6) + 5 = 5 m. Distance travelled from t = 0 to t = 3 s is d_1 = |-4 - 5| = 9 m. Distance travelled from t = 3 to t = 6 s is d_2 = |5 - (-4)| = 9 m. Total distance travelled is D = d_1 + d_2 = 9 + 9 = 18 m. Average speed = 18 6 = 3 ms^ -1 Answer: 3

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