Example 3
A particle moves along a straight line and passes through a fixed point O. Its velocity,
v ms-1, t seconds after passing through the point O is given by .
(a) Calculate
(i) the initial velocity of the particle,
(ii) the instantaneous velocity, in ms-1, of the particle when t=5s,
(iii) the time, in seconds, when the instantaneous velocity, in ms-1, of the particle is 6ms-1.
Solution:
(a)(i) Hence, the initial velocity of the particle is -12ms-1.
(ii) Hence, the instantaneous velocity of the particle when t=5 is 3ms-1.
(iii) Hence, the time is 6 seconds when the instantaneous velocity of the particle is 6ms-1.
(b) Sketch the velocity-time graph to represent the movement of the particle for .