You are given the following equaton of motion x = 3 t3 + 8.

Question

Determine the average velocity at

between 2 and 3 seconds and the average velocity between 2.4 and 2.6 seconds

Answer 1

I will assume you mean x = 3t³ + 8 or, using function notation x(t) = 3t³ + 8 then the average velocity is calculated using:

v_avg = [x(t₂) - x(t₁)}/(t₂ - t₁)

t₁ = 2 and t₂ = 3

x(t₁) = x(2) = 3(2)³ + 8 = 3•8 + 8 = 32

x(t₂) = x(3) = 3(3)³ + 8 = 3•27 + 8 = 89

So v_avg = (89 - 32)/(3 - 2) = 57/1 = 57 units/sec (you didn't specify what the units of distance were)