Displacement of the particle is .

(a)

Average velocity of an object moving in the time interval : .

(i) Time interval is .

Average velocity on the interval is .

(ii) Time interval is .

Average velocity on the interval is .

.

(iii) Time interval is .

Average velocity on the interval is .

.

(iv) Time interval is .

Average velocity on the interval is .

.

(b)

Find instantaneous velocity at .

Instantaneous velocity at : .

Here .

Instantaneous velocity at is m/sec.

(c)

Graph:

Graph the function .

Draw the secant line in pink color, whose slope is average velocity over .

Draw the secant line in green color, whose slope is average velocity over . \ \

Draw the secant line in maroon color, whose slope is average velocity over .

Draw the secant line in pink color, whose slope is average velocity over .

Draw the tangent line to the curve at .

(a)

(i) Average velocity on the interval is .

(ii) Average velocity on the interval is .

(iii) Average velocity on the interval is .

(iv) Average velocity on the interval is .

(b) Instantaneous velocity at is m/sec.

(c) Graph of the function, secant line and tangent line is