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**AP Review Problems – Resistive Forces as Functions of Velocity**

AP C 1993 A car of mass m, initially at rest at time t = 0, is driven to the right, as shown above, along a straight, horizontal road with the engine causing a constant force Fo to be applied. While moving, the car encounters a resistance force equal to ‑kv, where v is the velocity of the car and k is a positive constant. a. The dot below represents the center of mass of the car. On this figure, draw and label vectors to represent all the forces acting on the car as it moves with a velocity v to the right.

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**AP Review Problems – Resistive Forces as Functions of Velocity**

b. Determine the horizontal acceleration of the car in terms of k, v, Fo, and m.

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**AP Review Problems – Resistive Forces as Functions of Velocity**

c. Derive the equation expressing the velocity of the car as a function of time t in terms of k, Fo, and m. Separable, first order differential equation

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**AP Review Problems – Resistive Forces as Functions of Velocity**

c. Derive the equation expressing the velocity of the car as a function of time t in terms of k, Fo, and m. Let

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**AP Review Problems – Resistive Forces as Functions of Velocity**

c. Derive the equation expressing the velocity of the car as a function of time t in terms of k, Fo, and m. But

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**AP Review Problems – Resistive Forces as Functions of Velocity**

c. Derive the equation expressing the velocity of the car as a function of time t in terms of k, Fo, and m.

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**AP Review Problems – Resistive Forces as Functions of Velocity**

d. On the axis below, sketch a graph of the car’s velocity v as a function of time t. Label important values on the vertical axis.

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**AP Review Problems – Resistive Forces as Functions of Velocity**

e. On the axis below, sketch a graph of the car’s acceleration a as a function of time t. Label important values on the vertical axis.

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**AP Review Problems – Resistive Forces as Functions of Velocity**

e. On the axis below, sketch a graph of the car’s acceleration a as a function of time t. Label important values on the vertical axis. Two Methods

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**AP Review Problems – Resistive Forces as Functions of Velocity**

e. On the axis below, sketch a graph of the car’s acceleration a as a function of time t. Label important values on the vertical axis. Two Methods Substitute v from (c) into a from (b)

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**AP Review Problems – Resistive Forces as Functions of Velocity**

e. On the axis below, sketch a graph of the car’s acceleration a as a function of time t. Label important values on the vertical axis.

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If the sum of all the forces acting on a moving object is zero, the object will (1) slow down and stop (2) change the direction of its motion (3) accelerate.

If the sum of all the forces acting on a moving object is zero, the object will (1) slow down and stop (2) change the direction of its motion (3) accelerate.

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