# AVERAGE VELOCITY AND INTANTANEOUS VELOCITY WORKSHEET

Problem 1 :

A particle moves along a straight line in such a way that after t seconds its distance from the origin is

s = 2t2 + 3t meters

(i) Find the average velocity between t = 3 and t = 6 seconds.

(ii) Find the instantaneous velocities at t = 3 and t = 6 seconds.

Solution

Problem 2 :

A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of

s = 16t2

in t seconds.

(i) How long does the camera fall before it hits the ground?

(ii) What is the average velocity with which the camera falls during the last 2 seconds?

(iii) What is the instantaneous velocity of the camera when it hits the ground?

Solution

Problem 3 :

If the volume of a cube of side length x is v = x3 . Find the rate of change of the volume with respect to x when x = 5 units.

Solution

Problem 4 :

If the mass m(x) (in kilograms) of a thin rod of length x (in meters) is given by, m(x) = √3x then what is the rate of change of mass with respect to the length when it is x = 3 and x = 27 meters

Solution

1)  i)  the average velocity is 21 m/sec.

ii)  At t = 3, s'(3) = 15 m/sec

At t = 6, s'(6) =  27 m/sec

2)  i)  t = 5

ii)  in last two seconds the velocity is 128 ft/sec.

iii)  160 ft/sec

3)   75 units

4)  i)  m'(3) = 1/2

ii)  m'(27) = 1/6

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