Question

An object moves along the x axis according to the equation x(t)= (3.00t 2 - 2.00t + 3.00) m, where t is in seconds. Determine

(a) the instantaneous velocity at t = 2.00 s and t = 3.00 s, 

(b) the average acceleration between t = 2.00 s and t = 3.00 s,

(c) the instantaneous acceleration at t = 3.00 s

Answer 1

a)

$v=\frac{dx}{dt}=6t-2,$

$v(t=2)=10~\frac ms,$

$v(t=3)=16~\frac ms,$

b)

$a=\frac{v_3-v_2}{t_3-t_2}=\frac{16-10}{3-2}=6~\frac m{s^2},$

c)

$a=\frac{dv}{dt}=6~\frac m{s^2}.$