EXERCISE . . A particle moves along a straight line in such a way that after t seconds its distance from the origin is s metres. (i) Find the average velocity between t = and t = seconds.
(ii) Find the instantaneous velocities at t = and t = seconds. . A camera is accidentally knocked off an edge of a cliff ft high. The camera falls a distance of s = 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 seconds? (iii) What is the instantaneous velocity of the camera when it hits the ground? .
A particle moves along a line according to the law s t ( ) = , where t ≥ . (i) At what times the particle changes direction? (ii) Find the total distance travelled by the particle in the first seconds. (iii) Find the particle’s acceleration each time the velocity is zero.
. If the volume of a cube of side length x is v . Find the rate of change of the volume with respect to x when x = units . .
If the mass m x ( ) (in kilograms) of a thin rod of length x (in metres) is given by, m x ( ) = then what is the rate of change of mass with respect to the length when it is x = and x = metres. . A stone is dropped into a pond causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate at cm per second.
When the radius is cm find the rate of changing of the total area of the disturbed water? . A beacon makes one revolution every seconds. It is located on a ship which is anchored km from a straight shore line.
How fast is the beam moving