Question

N a time of t seconds, a particle moves a distance of s meters from its starting point, where s=10⁢t3.

Find the average velocity between t =1and t=1+h if:
i. h=0.1
ii. h=0.01
iii. h=0.001

Answer 1

i. Average velocity = 33.1 m/s

ii. Average velocity = 30 m/s

iii. Average velocity = 30 m/s

Step-by-step explanation:

Hi there!

The average velocity is calculated as follows:

Average velocity = Δs / Δt

Where:

Δs = traveled distance = final position - initial position

Δt = elapsed time = final time - initial time

i. Let´s evaluate s(t) at t = 1 and t = 1 + 0.1 = 1.1

s(1) = 10 · (1)³ = 10 m

s(1.1) = 10 · (1.1)³ = 13.31 m

Average velocity = (s(1.1) - s(1)) / (1.1 s - 1)

Average velocity = (13.31 m - 10 m) / (1.1 s - 1 s) = 33.1 m/s

ii. s(1.01) =10 · (1.01)³ = 10.3 m

Average velocity = (10.3 m - 10 m) / (1.01 - 1) = 30 m/s

iii. s(1.001) = 10 · (1.001)³ = 10.03 m

Average velocity = (10.03 m - 10 m) / (1.001 - 1) = 30 m/s