The period of an oscillating particle is 32 s, and its amplitude is 15 cm. at t = 0, it is at its equilibrium position. find the distances traveled during these intervals. (a) t = 0 to t = 8 s

At t=0, the particle was at its equilibrium position. The time period is 32 seconds, so in 8 seconds, it will reach the extreme location once, and hence, in 8 seconds, it will cover a distance equivalent to its amplitude.