A particle is projected from the origin at t=0 and its velocity as a function of time is given by v(t)=10e−0.5t+5t in metres per second.
(a) Obtain the expression for its instantaneous acceleration.
(b) Determine the exact time (in seconds) at which the acceleration becomes zero.
(c) Calculate the displacement of the particle from t=0 to the instant found in part (b).