A quick note on speed. The idea of differentiating speed to determine where it is increasing or decreasing is perfectly reasonable. . Then, Since the denominator is positive, and speed is increasing when and have the same sign, and and speed is decreasing when they have different signs. As a practical matter, this is the…
The parametric/vector equation questions only concern motion in a plane. In the plane, the position of a moving object as a function of time, t, can be specified by a pair of parametric equations or the equivalent vector . The path is the curve traced by the parametric equations or the tips of the position vector. . The velocity of the movement…
We continue the discussion of the various type questions on the AP Calculus Exams with linear motion questions. “A particle (or car, or bicycle) moves on a number line ….” These questions may give the position equation, the velocity equation (most often), or the acceleration equation of something that is moving, along with an initial…
AP Type Questions 4 These questions may give the position equation, the velocity equation or the acceleration equation of something that is moving, along with an initial condition. The questions ask for information about motion of the particle: its direction, when it changes direction, its maximum position in one direction (farthest left or right), its…
Speed is the absolute value of velocity: speed = . This is the definition of speed, but hardly enough to be sure students know about speed and its relationship to velocity and acceleration. Velocity is a vector quantity; that is, it had both a direction and a magnitude. The magnitude of velocity vector is the speed.…
Calculus is about things that are changing. Certainly, things that move are changing, changing their position, velocity and acceleration. Most calculus textbooks deal with thing being dropped or thrown up into the air. This is called as uniformly accelerated motion since the acceleration is due to gravity and is a constant. While this is a good place…
