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Variable acceleration and projectiles

Mechanics · Lesson 5 of 6

Lesson 5 of 6

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Lesson 5 of 6 · Mechanics

Variable acceleration and projectiles

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use the relationships $v=\dfrac{\mathrm{d}x}{\mathrm{d}t}$, $a=\dfrac{\mathrm{d}v}{\mathrm{d}t}$ and $a=v\dfrac{\mathrm{d}v}{\mathrm{d}x}$ for motion in a straight line with variable acceleration
differentiate displacement or velocity functions with respect to time to obtain velocity and acceleration, and integrate acceleration or velocity functions to obtain velocity or displacement using given conditions

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model projectile motion as motion under constant downward acceleration with no air resistance, and resolve initial velocity into horizontal and vertical components

use the independence of horizontal and vertical motion to find time of flight, range, greatest height, speed and direction at a given time or position

form and use Cartesian equations of projectile paths where required, including elimination of the parameter $t$

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