Mathematics

Problem

For a particle moving in a straight line, the velocity varies with time according to

v(t)=3t^2-12t+5

(SI units) for

0\le t\le5\,\text{s}

. a. (i) Sketch the

v

–

t

curve for the given time interval, clearly indicating the intercepts on the axes and the turning point. b. (ii) Calculate the instantaneous acceleration at

t=1\,\text{s}

and at

t=4\,\text{s}

. c. (iii) At each of the two instants above, state whether the particle is speeding up or slowing down and give a reason based on your results.

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