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

$x(t)=x_0+\underset{0}{\overset{t}{\int }}v(t)dt$

$v(t)=v_0+\underset{0}{\overset{t}{\int }}a(t)dt$

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

$a_{\parallel }=0$

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

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