UNFINISHED_AP Physics C Mechanics EXAM REVIEW

created 2025; EHS- UNFINISHED

vectors

quantities with magnitude and direction; ex- velocity, displacement, acceleration, force, momentum

can be written in component form: v= ai +bj+ ck

scalar

quantities with only a magnitude; ex- distance, speed, mass, energy, temperature, time

Dot Product (vector multiplication)

method 1: A*B = |A||B|cosθ

method 2: A*B= A_xB_x + A_yB_y + A_zB_z

produces a scalar

Cross Product (vector multiplication)

method 1: |AxB| = |A||B| sinθ

method 2: if A= A_xi + A_yj + A_zk and B= B_xi + B_yj + B_zk

then AxB= (A_yB_z - A_zB_y)i - (A_xB_z + A_zB_x)j + (A_xB_y - A_yB_x)j

produces a vector

average displacement, velocity, and acceleration

displacement: ∆x=(x_f - x_i) units: m

velocity: ∆v= ∆x/t units: m/s

acceleration: ∆a= ∆v/t units: m/s²

instantaneous displacement, velocity, and acceleration

displacement: x(t)= ∫v(t) dt

velocity: v_inst= dx/dt; v(t)= ∫a(t) dt

acceleration: a_inst=dv/dt OR a_inst=d²x/dt²

graphical representation of position, velocity, and acceleration

slope of x(t) = v(t)

slope of v(t) = a(t)

area under curve of a(t) = v(t)

area under curve of v(t) = x(t)

how to linearize data in desmos

steps

• add table, insert values, and adjust window

• determine the type of non-linear relationship (ex: inverse, square, inv-square, root, inv-root, quadratic, log, exponential)

• create new variables to represent the transformation

• plot the new data points

• draw a line of best fit

non-linear power function relationship examples (c is constant):

• inverse: y= c/x

• square: y= cx²

• inv-square: y= c/x²

• root: y= c√x

• inv-root: y=c/√x

kinematic equations for constant acceleration

v_f= v_i + at

x= x_i + v_it + 1/2at²

v_f²= v_i² + 2a(x_f - x_i)

x= 1/2(v_i + v_f)t

only when acceleration is constant!!

NOTE: START AT 1.4 DAILY VIDEOS