2.9.A—Describe the motion of an object subject to a resistive force

Describe the motion of an object subject to a resistive force.

• A resistive force is defined as a velocitydependent force in the opposite direction of an object’s velocity, for example:  =−Fk vr
• Applying Newton’s second law to an object upon which a resistive force is exerted results in a differential equation for velocity.
  • i. Using the method of separation of variables, the velocity can be determined by integrating over the proper limits of integration.
  • ii. The acceleration or position of a moving object that is subject to a velocity-dependent force may be determined using initial conditions of the object and methods of calculus, once a function for velocity is determined.
  • iii. The position, velocity, and acceleration as functions of time of an object under the influenc  e  of a resistive force of the form Fk vr =− are exponential and have asymptotes that are determined by the initial conditions of the object and the forces exerted on the object.
• Terminal velocity is defined as the maximum speed achieved by an object moving under the influence of a constant force and a resistive force that are exerted on the object in opposite directions. The terminal condition is reached when the net force exerted on the object is zero. TOPIC 2.9 Resistive Forces TOPIC 2.10 Circular Motion