AP Caculus AB Free Response: Particle Motion
how do you find when the particle changes directions?
Determine where the velocity curve changes signs (where it crosses the x-axis)
How do you determine if a particle is moving away from or towards the origin at a given time?
Evaluate s(t) and v(t). If the signs are the same, it's moving away from the origin. If the signs are different, it's moving toward the origin.
How do you determine if a particle is monied left or right?
If the velocity is negative, the particle is moving left. if the velocity is positive, the particle is moving right.
How do you find the change of position/distance from the velocity?
Integrate velocity over the time interval of interest ∫^b_a v(t)dt.
How do you find the times when a particle is at a specific position?
Set the position function equal to specified position and solve for t.
How do you find the times when a particle's acceleration is at a specific value?
Set the velocity function equal to the specified value and solve for t.
What is the origin?
The origin refers to zero on the number line
How do you find where a particle's acceleration is positive or negative?
find the critical values of velocity. Then create a sign chart using the critical values and the velocity function.
how do you find where a particle's velocity is positive or negative?
find the critical values of velocity. Then create a sign chart using the critical values and the velocity function.
how do you determine if a particle is speeding up or slowing down?
if velocity and acceleration have the same sigh, the particle is speeding up. If the signs are different, the particle is slowing down.
How do you find the position of a particle at a given time given velocity function?
s(0) + ∫₀ⁿ v(t)dt where t is the given time and s(0) is the initial position.
how of you find the times when a particle's acceleration is at a specific value?
set the acceleration function equal to the specified value and solve for t.
What is the difference between velocity and speed?
speed is the absolute value of velocity. Velocity is concerned with direction, speed is not. (speed cannot be negative)
What does the derivative of velocity tell us about the particle?
the acceleration of the partible
What does the derivative of position tell us about the particle?
the velocity of the particle
What is the difference between finding total distance traveled and total displacement?
total distance is found by integrating the speed function. total displacement is found by integrating the velocity function.
How do you find the total distance that a particle has traveled?
use integration to find the area under the speed curve. Speed is |velocity|
What are the critical values?
when a function equals zero or is undefined
What is the formula for average speed of a particle?
∆distance/∆time