4.6 Integration (A-level only)

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Question 26

A small object is dropped from a high altitude and falls vertically towards the ground.

Using a simple model of constant acceleration, a student predicts that the velocity of the object, exactly 5 seconds after being released from rest, is $s−15g\text{ m s}^{-1}$ . Show how the student has obtained this prediction.

[1]

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

a = g - 0.2 v

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

[5]

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

[2]

A small object is dropped from a high altitude and falls vertically towards the ground.

[1]

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

a = g - 0.2 v

where $s−1v\text{ m s}^{-1}$ is the velocity of the object 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 26

Markscheme

4.6 Integration (A-level only)

Question 26

Markscheme

4.6 Integration (A-level only)

Question 26

4.6 Integration (A-level only) Questions

4.6 Integration (A-level only)

Question 26

4.6 Integration (A-level only) Questions