Mathematics

Problem

The velocity of a body moving along a straight line is given by

v(t)=\dfrac{10t}{t+2}

(SI units) for

0\le t\le10\,\text{s}

. a. (i) Obtain an expression for the acceleration

a(t)

as a function of time. b. (ii) Evaluate

a(t)

t=0\,\text{s}

t=2\,\text{s}

and

t=8\,\text{s}

. c. (iii) Using your answers, comment briefly on how the magnitude and sign of acceleration vary with time and what this implies about the motion.