Quick questions on Rectilinear motion with differential equations: variable forces, resisted motion and terminal velocity - SQA Advanced Higher Mathematics of Mechanics

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is sign of the resistance?

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Resistance always opposes the motion, so it has the opposite sign to the velocity in the equation of motion. For a falling body with down positive, resistance is subtracted from the weight.

What is q1?

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A particle has

\dfrac{dv}{dt} = -2v

and starts at

v = 5

m s

^{-1}

. Find

v

as a function of

t

. [3 marks]

What is q2?

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A body falls under gravity against resistance

3v^2

per unit mass. Find its terminal velocity (

g = 9.8

). [2 marks]

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