Motion

A change in the location of an object, as measured by and observer

Graphs

Position Time

Constant Velocity, where slope is equal to the Velocity Exponential, Velocity is not constant, meaning it is accelerating.

Velocity Time

Constant Acceleration. Slope is equal to the Acceleration. The area under the graph during the time interval is Displacement

Acceleration Time

Area under the graph during the time interval is Velocity

Motion in two Directions

[E 20° N] is the same thing as [N 70° E], the former is preferred.

Steps

1. Find component vectors and take the sum of them
2. Find Distance using Pythagorean’s Theorem
3. Find angle using SOH CAH TOA

Formulas for Motion in 2 directions

$\Delta {\vec{d}}_x=\Delta \vec{d}\cos \theta$ $\Delta {\vec{d}}_y=\Delta \vec{d}\sin \theta$

Projectiles

Any object that moves in response to Gravity along a two-dimensional curved trajectory

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Key Details

• Horizontal and vertical motion are independent.
• Horizontal motion (${\vec{V}}_{av}$) is constant. Meaning there is no Acceleration.
• Vertical Motion (${\vec{V}}_i$, ${\vec{V}}_f$) is not constant. There is Acceleration due to gravity.

When Problem-Solving

Horizontal Motion (x)	Vertical Motion (y)
${\vec{V}}_{av}$	$\vec{a}=-9.8m/s^2$
	${\vec{V}}_i=?$
	${\vec{V}}_f=?$
	$\Delta t=?$
$\Delta t$ is the same for both horizontal and vertical motion

IMPORTANT

You must set which directions are positive

When the projectile is lauched Horizontally

When the projectile is launched with no vertical displacement

When the projectile is launched with vertical displacement EXAM QUESTION