2022 Sabah on hold

A particle moves along a straight line and its velocity, v, is given by v=t(a-bt) where t is the time in second after passing through a fixed point O, while a and b are constants. The particle stops momentarily when t=2 s and its distance at that moment is 4 m to the right of O. (Assume motion to the right is positive) a) Find the value of a and of b.

By using the values of a and b in (a), b) i) find the value of t when the particle passes the point O again,

ii) sketch the velocity-time graph of the motion of the particle

iii) find the total distance travelled by the particle in the first three seconds.