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OCR A Level Mechanics - Motion Calculus

Motion Calculus - Variable Accelaration

OCR A H230/02 Jun 2024 AS Exam Q. 11 :   Calculator Allowed 10 marks in 12:00 min.
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OCR A H230/02 Jun 2022 AS Exam Q. 11 :   Calculator Allowed 9 marks in 10:48 min.
OCR A H240/03 Jun 2022 A2 Exam Q. 12 :   Calculator Allowed 13 marks in 15:36 min.
OCR A H240/03 Nov 2021 A2 Exam Q. 13 c :   Calculator Allowed 5 marks in 6:00 min.
OCR A H230/02 Nov 2020 AS Exam Q. 10 :   Calculator Allowed 6 marks in 7:12 min.
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OCR A H240/03 Jun 2019 A2 Exam Q. 10 :   Calculator Allowed 13 marks in 15:36 min.
OCR A H230/02 Jun 2018 AS Exam Q. 11 :   Calculator Allowed 13 marks in 15:36 min.
OCR A H240/03 Jun 2018 A2 Exam Q. 11 :   Calculator Allowed 10 marks in 12:00 min.
OCR A H230/02 Jun 2017 AS Sample Exam Q. 10 :   Calculator Allowed 10 marks in 12:00 min.
OCR A H240/03 Jun 2017 A2 Sample Exam Q. 11 :   Calculator Allowed 9 marks in 10:48 min.
Investigate Motion Calculus
If $\color{blue}{ s }$ represents the position ("displacement") of an object at time $\color{black}{ t }$ then
$\color{green}{ \large { v = { {ds} \over {dt} } } }$ represents its velocity and
$\color{red}{ \large { a = { {dv} \over {dt} } = { { {d^2} s } \over { d {t^2} } } } }$ represents its acceleration.

This display allows you to investigate corresponding displacement, velocity and acceleration; lined up with a red glider which you can drag.

The initial example is $\color{blue}{ s = {t^3} - 3 \, {t^2} + 7 }$. At what times are the velocity and acceleration zero.
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