4.6 Integration (A-level only)

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Question 62

An autonomous underwater vehicle (AUV) is released from the surface of the ocean and descends vertically towards the seabed.

Using a simple model of constant acceleration 0.25 m s^-2, a researcher predicts that the velocity of the AUV exactly 80 seconds after being released from rest is 20 m s^-1. Show how the researcher has obtained this prediction.

[1]

Using a refined model that accounts for fluid resistance, it is assumed that the AUV's acceleration, $\text{ m s}^{-2}$ , at time $t\,$ seconds after release is given by

a = 0.25 - 0.01 v

where $\text{ m s}^{-1}$ is the velocity of the AUV at time $t$ . Find an expression for $v\,$ in terms of $t$ .

[6]

Compare the behavior of $v\,$ as $\to \infty\,$ for both models.

[2]

An autonomous underwater vehicle (AUV) is released from the surface of the ocean and descends vertically towards the seabed.

[1]

Using a refined model that accounts for fluid resistance, it is assumed that the AUV's acceleration, $\text{ m s}^{-2}$ , at time $t\,$ seconds after release is given by

a = 0.25 - 0.01 v

where $\text{ m s}^{-1}$ is the velocity of the AUV at time $t$ . Find an expression for $v\,$ in terms of $t$ .

Compare the behavior of $v\,$ as $\to \infty\,$ for both models.

[2]

4.6 Integration (A-level only)

Question 62

Markscheme

4.6 Integration (A-level only)

Question 62

Markscheme

4.6 Integration (A-level only)

Question 62

4.6 Integration (A-level only) Questions

4.6 Integration (A-level only)

Question 62

4.6 Integration (A-level only) Questions