Question

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?

Answer 1

a)

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

b)

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

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

c)

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

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