Integrating with Respect to Time (HSC SSCE Mathematics Advanced): Quizzes

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Integrating with Respect to Time
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What is integration in the context of motion problems?

The reverse operation of differentiation

What do you obtain when you integrate the acceleration function aa?

The velocity function vv

Why must you add a constant when integrating in motion problems?

Differentiation removes constants

What is the approximate value of acceleration due to gravity gg near Earth's surface?

9.89.8 m/s²

If upwards is taken as positive, what is the acceleration function for a falling object?

a=−ga = -g

Can you use the formula v=u+atv = u + at in HSC Mathematics Advanced motion problems?

No, you must integrate from first principles

When is a particle stationary?

When v=0v = 0

If v=4tv = 4t and x=2x = 2 when t=0t = 0, what is the displacement function xx?

x=2t2+2x = 2t^2 + 2

If downwards is positive, what acceleration function describes a falling object?

a=ga = g

For a=e−2ta = e^{-2t} with initial v=0v = 0, what happens to velocity as tt increases?

It approaches a limiting velocity

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