PHYS 218 Exam 1

2D movement (x,y graph)

• Velocity is always tangent to path
• Acceleration points to concave side of a curve

1D movement (x,t graph)

• Velocity is slope of line tangent
• Acceleration: sign is determined by concavity (<0 cc↓, =0, >0 cc↑)

Equations of motion

General Acceleration

$x(t)=x_{0}+\int _{0}^{t}v(t)\ dt$

$v(t)=v_{0}+\int _{0}^{t}a(t)\ dt$

Constant Acceleration

$x(t)=x_{0}+v_{0}t+{\frac {a}{2}}t^{2}$

$v(t)=v_{0}+at$

Extra (derived) equations

${v(t)}^{2}={v_{0}}^{2}+2ax(x(t)-x_{0})$

$x(t)-x_{0}=\left({\frac {v_{0}+v(t)}{2}}\right)t$

Circular Motion

Uneven Speed

$a_{\perp }={\frac {v^{2}}{R}}$ Changes direction of movement, but keeps speed of object

$a_{\parallel }={\frac {dv}{dt}}$ Changes speed of object, but keeps direction.

Constant Speed

Period ($T$) = time needed for 1 revolution

Frequency ($f$) = ${\frac {1}{T}}$

$a_{\parallel }=0$

$|v|={\frac {2\pi R}{T}}$

$a_{\perp }={\frac {4\pi ^{2}R}{T^{2}}}=4\pi ^{2}Rf^{2}$