For a particle moving along the x-axis the velocity varies with time as v(t)=4t−t2 in SI units (t in seconds, v in m s−1) for 0≤t≤6s. The particle is at the origin at t=0. Answer the following:
a. (i) Show that the particle reverses its direction only once within the given time interval and find the instant at which this occurs.
b. (ii) Obtain the expression for displacement x(t) taking x(0)=0.
c. (iii) Calculate the net displacement of the particle at t=6s.
d. (iv) Determine the total distance travelled by the particle in the interval 0≤t≤6s.
e. (v) Compute the average speed and the average velocity for this interval.