A particle's position in metres over time is modelled by the function s(t) = 2t -...

 

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A particle's position in metres over time is modelled by the function s(t) = 2t - 15t, where t 0 in seconds. (a) If s(t) is the position function, then s'(t) = v(t) is the velocity function. Find the velocity function for the particle and verify the result with Maple. (b) When is the particle at rest? (c) Create a plot of s(t) with Maple. Does your graph agree with your answer from part (b)? Explain. (d) If s(t) is the position function, then s"(t): == a(t) is the acceleration function. Find the acceleration function for the particle and verify the result with Maple. (e) The particle is accelerating when v and a have the same sign. When is the particle acceler- ating? (f) Create a plot of v(t) and a(t) together on the same grid with Maple. Does your graph agree with your answer from part (e)? Explain. A particle's position in metres over time is modelled by the function s(t) = 2t - 15t, where t 0 in seconds. (a) If s(t) is the position function, then s'(t) = v(t) is the velocity function. Find the velocity function for the particle and verify the result with Maple. (b) When is the particle at rest? (c) Create a plot of s(t) with Maple. Does your graph agree with your answer from part (b)? Explain. (d) If s(t) is the position function, then s"(t): == a(t) is the acceleration function. Find the acceleration function for the particle and verify the result with Maple. (e) The particle is accelerating when v and a have the same sign. When is the particle acceler- ating? (f) Create a plot of v(t) and a(t) together on the same grid with Maple. Does your graph agree with your answer from part (e)? Explain.