4.6 Integration (A-level only)

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Question 37

A high-performance motorboat starts from rest at a marker on a calm lake and accelerates in a straight line.

Using a simple model of constant acceleration $\text{ m s}^{-2}$ , a technician predicts that the velocity of the boat, exactly 5 seconds after starting from rest, is $\text{ m s}^{-1}$ . Show how the technician obtained this prediction.

[2]

Using a refined model that accounts for water resistance, the boat's acceleration, $\text{ m s}^{-2}$ , at time $t$ seconds after starting is given by the differential equation

\frac{dv}{dt} = 2.4 - 0.4v

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

[5]

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

[2]

A high-performance motorboat starts from rest at a marker on a calm lake and accelerates in a straight line.

[2]

Using a refined model that accounts for water resistance, the boat's acceleration, $\text{ m s}^{-2}$ , at time $t$ seconds after starting is given by the differential equation

\frac{dv}{dt} = 2.4 - 0.4v

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

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

[2]

4.6 Integration (A-level only)

Question 37

Markscheme

4.6 Integration (A-level only)

Question 37

Markscheme

4.6 Integration (A-level only)

Question 37

4.6 Integration (A-level only) Questions

4.6 Integration (A-level only)

Question 37

4.6 Integration (A-level only) Questions