Question

1) A particle moves along the x axis according to the equation x(t) = 3t ^ 2 - 2t + 3 , where x is in meters and t is in seconds. a) what is the particle position at t=2s^ prime b) what is the particle displacement between t = 4s and t=2s^ prime ? c) what is the particle average velocity between t = 4s and t = 2s d) what is the particle velocity as a function of t? e) what is the particle velocity at t = 3s ? f) what is the particle average acceleration between t = 3s and t = 1s ? g) what is the particle acceleration as a function of t? h) what is the particle acceleration at t = 3s ?

Answer 1

a)

$$x(2) = 3(2)^ 2 - 2(2)+ 3=11\ m$$

b)

$$x(4) = 3(4)^ 2 - 2(4)+ 3=43\ m\\s=43-11=32\ m$$

c)

$$v=\frac{32}{4-2}=16\frac{m}{s}$$

d)

$$v(t)=6t-2$$

e)

$$v(3)=6(3)-2=16\frac{m}{s}$$

f)

$$a=6\frac{m}{s^2}$$

g)

$$a(t)=6\frac{m}{s^2}$$

h)

$$a(3)=6\frac{m}{s^2}$$