Question #271892

A position function of a moving particle is given as a function of time, ~r(t) = (2t 2 + 3t)ˆi + (5t 3 + 2t)ˆj m. (1) (a) What is the average velocity between time t1 = 2 s and t2 = 5 s? (b) What is the average acceleration between time t1 = 2 s and t2 = 5s? (c) What is the instantaneous acceleration of the particle at t2 = 5 s?


1
Expert's answer
2021-11-29T11:46:16-0500

a)

<v>=65i+635j14i44j3=17i+197j,<\vec v>=\frac{65\vec i+635\vec j-14\vec i-44\vec j}{3}=17\vec i+197\vec j,

b)

v=(4t+3)i+(15t2+2)j,\vec v=(4t+3)\vec i+(15t^2+2)\vec j,

<a>=23i+377j11i62j3=4i+105j,<\vec a>=\frac{23\vec i+377\vec j-11\vec i-62\vec j}{3}=4\vec i+105\vec j,

c)

a=4i+30tj,\vec a=4\vec i+30t\vec j,

a(5)=4i+150j.\vec a(5)=4\vec i+150\vec j.


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