# Calculus particle motion problems

AP Calculus Unit 5 – Applications of the Derivative – Part 2. Day 4 & 5 Notes: Particle Motion Problems. Average and Instantaneous Velocity Example 1: A particle’s position is given by the function. p(t) e. t sin t. , where p(t) is measured in centimeters and t is measured in seconds. Particle Motion Problems Particle motion problems deal with particles that are moving along the x – or y – axis. Thus, we are speaking of horizontal or vertical movement. The position, velocity, or acceleration of a particle’s motion are DEFINED by functions, but the particle DOES NOT move along the graph of the function. It moves along an axis. AP Calculus Rectilinear Motion Problems Calculator 1. A particle moves along a straight line. For 0≤ ≤5, the velocity of the particle is given by 𝑣( )= −2+( 2+3 ) 6 ⁄5− 3, and the position of the particle is given by s(t). It is known that s(0) = 10. a. Find all values of t in the interval 2≤ ≤4 for which the speed of the ... CALCULUS WORKSHEET ON PARTICLE MOTION If s f t is the position function of a particle that is moving in a straight line, then the instantaneous velocity of the particle is the rate of change of the displacement with respect to For this type of motion, a particle is only allowed to move along the radial R-direction for a given angle θ. For a particle P defined in polar coordinates (as shown below), we can derive a general equation for its radial velocity ( v r ), radial acceleration ( a r ), circumferential velocity ( v c ), and circumferential acceleration ( a c ).