A particle moves along a straight line, and its displacement at time t seconds is denoted by s(t) metres.
Answer the following questions relating velocity and acceleration to the calculus of motion:
(i) Define velocity and acceleration in terms of derivatives of displacement with respect to time.
(ii) State what information about the motion of the particle is conveyed by the sign of acceleration when the velocity is positive.
(iii) If s(t)=5t−2, determine the acceleration of the particle and interpret your result physically.