Instantaneous Velocity

Question

To estimate the instantaneous velocity when t = 1, we need to estimate
vave = 8.28 − 1.86h
when h approaches ? .

This yields
vave =  m/s.

Answer 1

Steps to find the instantaneous velocity at t = 1:

1. Write the average‐velocity formula around t = 1:

v_ave(h) = [s(1 + h) − s(1)] / h

2. Substitute the given difference:

s(1 + h) − s(1) = 8.28 h − 1.86 h²

⇒ v_ave(h) = (8.28 h − 1.86 h²) / h

= 8.28 − 1.86 h

3. Define the instantaneous velocity as the limit:

v(1) = lim₍h→0₎ v_ave(h)

4. Take the limit as h → 0:

v(1) = lim₍h→0₎ (8.28 − 1.86 h)

= 8.28 m/s