Question

The table shows the position of the cyclist

t (seconds)	0	1	2	3	4	5
s (meters)	0	1.1	4.6	10.1	17.9	25.5

(a) Find the average velocity for each time period.

(i) [1, 3] __ m/s

(ii) [2, 3] __ m/s

(iii) [3, 5] __ m/s

(iv) [3, 4] __ m/s

(b) Estimate the instantaneous velocity when t = 3.

__ m/s

Answer 1

(a) To find the average velocity for each time period, you can use the formula for average velocity:

Average Velocity (m/s) = Δs / Δt

Where Δs is the change in position (final position - initial position) and Δt is the change in time (final time - initial time).

(i) [1, 3]: Δs = s(3) - s(1) = 10.1 - 1.1 = 9.0 meters Δt = 3 - 1 = 2 seconds

Average Velocity = Δs / Δt = 9.0 m / 2 s = 4.5 m/s

(ii) [2, 3]: Δs = s(3) - s(2) = 10.1 - 4.6 = 5.5 meters Δt = 3 - 2 = 1 second

Average Velocity = Δs / Δt = 5.5 m / 1 s = 5.5 m/s

(iii) [3, 5]: Δs = s(5) - s(3) = 25.5 - 10.1 = 15.4 meters Δt = 5 - 3 = 2 seconds

Average Velocity = Δs / Δt = 15.4 m / 2 s = 7.7 m/s

(iv) [3, 4]: Δs = s(4) - s(3) = 17.9 - 10.1 = 7.8 meters Δt = 4 - 3 = 1 second

Average Velocity = Δs / Δt = 7.8 m / 1 s = 7.8 m/s

(b) To estimate the instantaneous velocity at t = 3 seconds, you can look at the average velocity over a very short time interval that includes t = 3. In this case, you can use the interval [2, 3] because it's very close to t = 3.

Δs = s(3) - s(2) = 10.1 - 4.6 = 5.5 meters Δt = 3 - 2 = 1 second

Instantaneous Velocity ≈ Δs / Δt ≈ 5.5 m / 1 s = 5.5 m/s

So, the estimated instantaneous velocity at t = 3 seconds is approximately 5.5 m/s.