Lesson Section 6 3 5 Intro to Differential

Lesson: _____ Section 6. 3, 5 Intro to Differential Equations & The Equations of Motion An equation containing derivatives is called a “differential equation. ” Ex. A car is driving in a straight line at a constant velocity of 50 mph. If s is the distance of the car from a fixed point, and t is time in hours, then This is called “rectilinear motion” (straight line) This is called a “differential equation” for function s. This says the derivative of s is 50. The “solution” to the diff. eq. is function s, which is the antiderivative of 50

Ex. An apple is dropped from a 100 ft building. Find position and velocity as a function of time. When does it hit the ground? How fast is is going when it hits? If distance is in feet, and time is in seconds, then… This diff. eq. represents the acceleration. Why is it negative? Let’s rewrite this function for velocity as a differential equation for position

When does it hit the ground? Think about it. What does it mean in terms of position when the apple hits the ground? How fast is is going when it hits? Should this be negative? Yes! Our position is decreasing which means a negative rate of change. • See also p. 295 example 2 (make sure to look at this!). Note initial velocity is given. How do we find the “highest point” using the derivative? • Take a minute to READ 6. 5 (history of the equations of motion)