Exploring Free-Response Questions in AP Calculus AB

In this video tutorial, teachers Verge Cornelius and Mark Corelli guide students through a particle motion problem involving a particle P moving along the y-axis. The session is divided into four parts: calculating acceleration at a specific time, analyzing speed changes, determining position and movement relative to the origin, and comparing velocities of two particles. The tutorial emphasizes the use of calculators for solving complex derivatives and integrals, and highlights the importance of clear communication in mathematical reasoning.

What is the initial position of particle P along the y-axis?

• y = 2

• y = 0

• y = 1

• y = -1

How is the acceleration of particle P at time T = 1.3 calculated?

• By integrating the velocity function

• By squaring the velocity function

• By differentiating the position function

• By differentiating the velocity function

If both velocity and acceleration have the same sign at a specific time, what can be inferred about the particle's speed?

• Cannot determine

• Speed is increasing

• Speed is decreasing

• Speed is constant

What method is used to determine if the speed of particle P is increasing at time T = 1.3?

• Comparing the signs of position and velocity

• Comparing the signs of velocity and acceleration

• Differentiating the velocity function again

• Integrating the acceleration function

What does the position value at T = 1.3 indicate about particle P's motion?

• Stationary at the origin

• Moving towards the origin

• Oscillating around the origin

• Moving away from the origin

How is the position of particle P at time T = 1.3 found?

• By setting the velocity to zero and solving for position

• By differentiating the velocity function

• By squaring the velocity function

• By integrating the velocity function from 0 to 1.3

What does a negative velocity at T = 1.3 imply about particle P's direction?

• It is moving in a positive direction

• It is stationary

• It is moving away from the origin

• It is moving towards the origin

What is the first time when particles P and Q have the same velocity?

• T = 1.300

• T = 0.680

• T = 0.500

• T = 1.000

How do you find the velocity of particle Q?

• By differentiating the position function Q of T

• By integrating the position function Q of T

• By evaluating Q of T at specific times

• By plotting Q of T on a graph

Which tool is emphasized as crucial for solving problems in this tutorial?

• A ruler

• Graph paper

• A calculator

• A protractor