A particle moves along a straight line. Its velocity at time t t\,t seconds is v=6cos(πt2) m s−1\displaystyle v=6\cos\left(\frac{\pi t}{2}\right)\text{ m s}^{-1}v=6cos(2πt) m s−1, where 0≤t≤40\leq t\leq40≤t≤4. The particle starts at the origin.
Find all the times in the interval at which the particle is instantaneously at rest.
Find the total distance travelled in the first 4 seconds, giving your answer in terms of π\piπ.