Suppose an object moves along the y axis so that its location is yequals f (x) equalsxsquaredplusx at time x (y is in meters, x is in seconds). Find (A) The average velocity (the average rate of change of y with respect to x) for x changing from 2 to 5. (B) The average velocity for x changing from 2 to 2plush. (C) The instantaneous velocity at xequals2 second. (A) The average velocity is 8 m/sec. (B) The average velocity is (nothing) m/sec. (C) The instantaneous velocity is 5 m/sec.

Given

y (x) = x² + x (x represents time in seconds)

A)

value of y at x = 2

= 2²+2 = 6 m

value of y at x = 5

= 5²+5 = 30 m

displacement = 30 - 6 = 24 m

Time duration = 5 - 2 = 3 s

average velocity

= displacement / Time duration

= 24 / 3 = 8 m / s

B) For x changing from x to x plus ie for small change in x:

value of y at x = 2

= 5

For small change in x, the value of y will again be 5 so displacement during small change in x will be zero. Hence average velocity will be zero.

C)

y (x) = x² + x

dy / dx = 2x + 1

dy / dx represents instantaneous velocity

so when x = 2

instantaneous velocity = 2 x 2 + 1

= 5 m / s