Problem 1 :
A particle moves along a straight line in such a way that after t seconds its distance from the origin is
s = 2t^{2} + 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.
Problem 2 :
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of
s = 16t^{2}
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?
Problem 3 :
If the volume of a cube of side length x is v = x^{3} . Find the rate of change of the volume with respect to x when x = 5 units.
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
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
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM