Basic Terms and Definitions
What is an axis of motion?
The frame of reference when observing a change in an object's position relative to a given observer
What is Δt, Δx, and Δv?
Change in time, displacement, and change in velocity
What is velocity with respect to a position vs. time graph?
Velocity is the slop of the graph (Δx/Δt)
Translating and Sketching the problem
If a jogger goes to the right 30 meters, and then to the left 40 meters, what is their distance traveled? What is their displacement?
Distance = 70 meters
Displacement = -10 meters
What is the difference between a scalar and a vector quantity?
A scalar quantity is only magnitude while a vector quantity is magnitude AND direction
What is the equation for average velocity?
vavg = (xf - xi)/Δt
What is acceleration with respect to a velocity vs. time graph?
Acceleration is the slope(Δv/Δt)
What is the second step of the problem solving framework?
Determine your known values
A car travels from point A to point B over a time span of 15 seconds. Point B is 45 meters from point A. What is the displacement? What is the change in time? What is the velocity?
Δx = 45 m
Δt = 15s
V = Δx/Δt = 45 m/15 s = 3 m/s
What is acceleration?
The change in velocity over time
What is the formula for average acceleration?
aavg = (vf - vi)/Δt
When Dr. Mason derived the equation for position using a velocity over time graph, what was the assumption and what was he doing?
The assumption was acceleration is constant and he was finding the area under the curve.
What is the third step in the problem solving framework?
Determine your unknown values and what you are trying to find
A biker travels 40 meters to the right over a time span of 5 seconds at a constant speed. They then travel 60 meters to the left over another 5 seconds, also at a constant speed. What is v1, v2, and vavg?
v1 = 40 m/ 5 s = 8 m/s
v2 = -60 m/ 5 s = -12 m/s
vavg = -20 m/ 10 s = -2 m/s
What is the difference between distance and displacement?
Distance is the total length traveled and is path dependent, while displacement is only the final position minus the initial position and is path independent.
What is the kinematic equation that equates position and includes the objects velocity and acceleration?
Δx = viΔt + 1/2*a*(Δt)2
or
xf = xi + viΔt + 1/2*a*(Δt)2
When given a position over time graph, what will the velocity over time graph look like?(Section 1 on CoLab)
A straight line that is positive
What is the fourth step in the problem solving framework?
Plan a solution
Assume acceleration is constant. Find the position from this velocity vs. time graph. (Section 3 on CoLab)
Δx = AR + AT = b*h + 1/2*b*h
= 5*5 + 1/2*5*5
= 25 + 12.5
= 37.5 m
What is the difference between instantaneous velocity and average velocity?
Instantaneous velocity measures the velocity of an irritative step of a problem, while the average velocity looks at the velocity of the entire problem solely based on the initial position, final position, and time passed.
What is the fifth kinematic equation that does not require the change in time?
vf2 = vi2 + 2aΔx
When given a position over time graph, what will the velocity over time graph look like, and what will the acceleration over time graph look like?(Section 2 on CoLab)
Velocity is a linearly increasing line while acceleration is a constant, positive line.
What is the fifth step in the problem solving framework, and why do we use it?
Solve and check your answer. It organizes the problem solving method and gives you a clear track to work on when presented a problem.
A ball is initially traveling at 2 m/s. All of a sudden, it begins accelerating at a rate of 3 m/s2. If it travels for 5 seconds, at what point does it travel to from when it began accelerating?
xf = xi + viΔt + 1/2*a*(Δt)2
= 0 + (2m/s)*5s + 1/2*3m/s2*(5s)2
= 10m + 37.5m
= 47.5m