Class Notes 02 September Turn in HW / Pick up HW! Today: Draw origin / coordinate system Did you write the general eqn’s?? #1b: The car did not decelerate Today: One more f.f. example problem Graphical Methods Vectors

How many of the “fundamental four” equations can you remember? 0  1 2 3 4  5

Example A rocket is traveling upwards at 100. m/s. When it is 500. m above the Earth its booster turns off. How high above the Earth does the booster go? How long until it hits the ground? Part b) is solved easiest using x = x0 + v0t +(1/2)at2. Solving quadratic gives two solutions. Discuss the erroneous (non physical) answer. 1010. m, 24.56 s – 4.15s

Velocity at t = 2 s? So now we’ll zoom in (t = 1-3 s) Write velocity equation, with lim t0

Velocity at t = 2 s? Zoom in again (t = 1.9-2.1 s) Ave vel = Slope = … = –12 m/s

Ave vel is nearly constant! Velocity at t = 2 s? Slope = … = –13 m/s Ave vel is nearly constant! Notice Dt  0 the definition of instantaneous velocity, v = lim(x/t), can be written v = lim(vave).

Summarize Secant line slope gives average velocity Tangent line slope gives inst. velocity

Constant acceleration On a v-vs-t graph, I want to draw various situations where the acceleration is constant. For each I want you to think of a physical example that could be like that.

Constant acceleration I predict that some of these will be drawn.

Graphical Acceleration Consider vel-vs.-time graphs In much the same manner, the slope of the straight line connecting two points on a velocity-vs.-time curve gives the average acceleration. The slope of the tangent line gives the instantaneous acceleration Argue again with slope = rise/run = v/t, which is by definition the average acceleration. Similarly with the instantaneous acceleration.

Displacement from graph Consider a vel-vs.-time graph: The area under ANY velocity- vs.-time curve (between t1 and t2) is the displacement during that time interval. v v t t1 t2 v t t1 t2

Considering the test, which describes you? I feel very confidant I’ll do well I’ll be OK I’m a bit worried I’m very worried I think I’ll sleep in

Considering the test, what grade do you expect? High A Low-Mid A High B Low-Mid B High C Low-Mid C Failure

Oh joy! Our first test! 8:00 class arrive 5 min early No cell phones! Cell phone=0 55 minutes. ~1 page short answer (35-40%) 3 of 4 problems (60-65%) Work directly on the test paper Review sheet Online resources

Homework Read chapter 3.1-3.3 Homework on Canvas coming soon TEST WEDNESDAY (50pts) All of Chapter 1 and 2 Review sheet Practice quizzes, Old tests Know, not memorize, the funda- mental four equations!