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