2.3.3 Relating Position, Velocity, and Acceleration Vectors in Two Dimensions

Question 1

Relating Position, Velocity, and Acceleration Vectors in Two Dimensions

Answer 1

• The vector equations and contain information about motion in the x- and y-directions.•Drawing pictures with vectors is a useful way to visualize two-dimensional motion.
• Take the derivative of the components of the position vector to find the velocity vector; take the derivative of the components of the velocity vector to find the acceleration vector.

Question 2

note

Answer 2

• Motion in two dimensions is richer than motion in one dimension. The vector equations for acceleration and velocity contain information about motion in both the x- and y-directions.
• The position of an object as a function of time is given by the equation . You can find the equation for object’s velocity vector as a function of time by taking the time derivative of its position function:. Similarly, you can find the equation for the object’s acceleration vector as a function of time by taking the time derivative of its velocity function:.
• The object’s path is a parabola. The horizontal component of the velocity is constant in time: . The vertical component of velocity increases 10 m each second:. The object’s velocity vector is always tangent to its position function.
• Recall that the horizontal component of the object’s velocity is constant. As a result its acceleration has no horizontal. The vertical component of the velocity increases with time so there is a vertical component of the acceleration. The vertical component of the acceleration is constant in time: