02. Kinematics

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• Displacement is the distance travelled along a specified direction.
• Speed is the rate of change of distance travelled.
• Velocity is the rate of change of displacement.
• Acceleration is the rate of change of velocity.

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• $$v=u+at$$
• $$s=(\frac{u+v}{2})t$$
• $$s=ut+\frac{1}{2}at^2$$
• $$v^2=u^2+2as$$

s: displacement u: initial velocity v: final velocity a: acceleration t: time [/accordion] [accordion title="3. Two-Dimensional Motion"]

• Tip: Sometimes, you will require two equations to solve a kinematics problem. For a parabolic path in a projectile motion without resistive forces, you can draw a table such as the one below and fill in the blank with the information given in the question.

[caption id="attachment_1933" align="aligncenter" width="163"] Initial velocity at an angle[/caption]

• In the case where a projectile is launched at an angle $$\theta$$ to the horizontal and undergoes the acceleration of free fall, the various horizontal and vertical components of displacement, velocity and acceleration can be expressed in the following way:

	Horizontal	Vertical
displacement, s	$$(u \cos \theta)t$$	$$(u \sin \theta)t+\frac{1}{2}gt^2$$
initial velocity, u	$$u \cos \theta$$	$$u \sin \theta$$
initial velocity, v	$$u \cos \theta$$	$$u \sin \theta +gt$$
acceleration, a	0	$$g$$
time, t	same for	both dimensions

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