article moves according to a law of motion below, 0≤t<8, where t is measured in seconds and s in feet. s=f(t)=cos(4πt​)

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article moves according to a law of motion below, 0≤t<8, where t is measured in seconds and s in feet. s=f(t)=cos(4πt​) (a) Find the velocity at time t. v(t)= ft/s (b) What is the velocity after 7 s ? (Round your answer to three decimal places.) v(7)= ft/s (c) When is the particle at rest? t=s (smaller value) t= s (larger value) (d) When is the particle moving in the positive direction? ( ) (e) Find the total distance traveled during the first 8 s. feet (f) Draw a diagram to Illustrate the motion of the particle. (Do this on paper, Your instructor may ask you to turn in this graph.) (g) Find the acceleration at time t and after 7 s. (Round your answer to three decimal places.) a(t)= a(7)= fts2​ (h) Graph the position, velocity, and acceleration functions for 0≤t≤8. (Do this on paper, Your instructer may ask you to furn in this graph.) (1) When is the particle speeding up? (0≤t≤8)