The table shows the position of a cyclist.
t (seconds) 0 1 2 3 4 5
s (meters) 0 1.4 5.4 10.8 17.4 24.6
(a) Find the average velocity for each time period.
(i) [1, 3]
4.45
Incorrect: Your answer is incorrect.
m/s
(ii) [2, 3]
5.5
Incorrect: Your answer is incorrect.
m/s
(iii) [3, 5]
-7.2
Incorrect: Your answer is incorrect.
m/s
(iv) [3, 4]
-3.5
Incorrect: Your answer is incorrect.
m/s
(b) Estimate the instantaneous velocity when t = 3.
6.25
Incorrect: Your answer is incorrect.
10.8/3 = 3.6
(10.8-5.4)/1 = 5.4
(24.6-10.8)/2 = 6.9
(17.4-10.8)/1 = 6.6
(17.4-5.4)/2 = 6
To find the average velocity for each time period, we need to calculate the change in position (Δs) divided by the change in time (Δt).
(a)
(i) Average velocity for the time period [1, 3]:
Δs = s(3) - s(1) = 10.8 - 1.4 = 9.4 meters
Δt = 3 - 1 = 2 seconds
Average velocity = Δs / Δt = 9.4 / 2 = 4.7 m/s
(ii) Average velocity for the time period [2, 3]:
Δs = s(3) - s(2) = 10.8 - 5.4 = 5.4 meters
Δt = 3 - 2 = 1 second
Average velocity = Δs / Δt = 5.4 / 1 = 5.4 m/s
(iii) Average velocity for the time period [3, 5]:
Δs = s(5) - s(3) = 24.6 - 10.8 = 13.8 meters
Δt = 5 - 3 = 2 seconds
Average velocity = Δs / Δt = 13.8 / 2 = 6.9 m/s
(iv) Average velocity for the time period [3, 4]:
Δs = s(4) - s(3) = 17.4 - 10.8 = 6.6 meters
Δt = 4 - 3 = 1 second
Average velocity = Δs / Δt = 6.6 / 1 = 6.6 m/s
(b) To estimate the instantaneous velocity at t = 3, we can take the average velocity of the time period that is closest to t = 3. In this case, it would be the average velocity for the time period [2, 3].
Average velocity at t = 3 ≈ 5.4 m/s.
To find the average velocity for each time period, we need to calculate the change in position (s) divided by the change in time (t).
(i) [1, 3]:
Change in position (Δs) = s(3) - s(1) = 10.8 - 1.4 = 9.4 meters
Change in time (Δt) = t(3) - t(1) = 3 - 1 = 2 seconds
Average velocity = Δs/Δt = 9.4/2 = 4.7 m/s
(ii) [2, 3]:
Change in position (Δs) = s(3) - s(2) = 10.8 - 5.4 = 5.4 meters
Change in time (Δt) = t(3) - t(2) = 3 - 2 = 1 second
Average velocity = Δs/Δt = 5.4/1 = 5.4 m/s
(iii) [3, 5]:
Change in position (Δs) = s(5) - s(3) = 24.6 - 10.8 = 13.8 meters
Change in time (Δt) = t(5) - t(3) = 5 - 3 = 2 seconds
Average velocity = Δs/Δt = 13.8/2 = 6.9 m/s
(iv) [3, 4]:
Change in position (Δs) = s(4) - s(3) = 17.4 - 10.8 = 6.6 meters
Change in time (Δt) = t(4) - t(3) = 4 - 3 = 1 second
Average velocity = Δs/Δt = 6.6/1 = 6.6 m/s
(b) To estimate the instantaneous velocity at t = 3, we can take the average velocity of the time period [2, 3] and [3, 4]:
Average velocity at t = 3 ≈ (5.4 m/s + 6.6 m/s) / 2 = 11.2 / 2 = 5.6 m/s