Aparticle moves according to a law of motion s f(t) t5- 15t2 + 48t, t2 0, where t is measured in seconds and s in feet (a) find the velocity at time t. v(t) x ft/s (b) what is the velocity after 1 s? x ft/s v(1)3 (c) when is the particle at rest? (smaller value) x (larger value) x (d) when is the particle moving in the positive direction? (enter your answers in ascending order. if you need to use -o or o, enter -infinity or infinity.) ) (e) find the total distance traveled during the first 9 s feet (f) draw a diagram to illustrate the motion of the particle. (do this on paper, not to turn in.) (g) find the acceleration at time t and after 1 s. a(t) ft/s2 a(1)= sts 9. (do this on paper. your instructor may ask you to turn in this graph.) (h) graph the position, velocity, and acceleration functions for (i) when the particle speeding up? (enter your answers in ascending order. if you need to use -o or , enter -infinity or infinity.) ( ) when it slowing down?