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

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• 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.
• 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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