Acceleration+in+One+Dimension

=Acceleration in One and Two Dimensions=

1. Why do we need to know about acceleration?
- real life does not consist of objects speeding up or stopping instantly - although it is a good place to start in physics - used for objects that are speeding up or slowing down; the speed changes gradually, not all of a sudden - graph of distance vs time will look like a curve; often like a parabola. And graphs of speed vs time will look like ...

2. How to determine the instantaneous speed (already covered; this is for review)
- use your ruler to draw a tangent line to the curve; a tangent line touches the point before it touches the rest of the curve - people will have slightly different lines for the same point on a curve, but the slopes will be within the same range - draw a right-angled triangle around your sloped line and determine the slope of the tangent. - you will notice that steep slopes represent high speeds, horizontal lines represent a speed of zero; just like the graphs for uniform motion. follow [|this link] for a more technical look at instantaneous speed (especially the first 5 - 6 graphs).

3. Acceleration - the change in an object's velocity over time
-Acceleration occurs when the speed or direction of an object changes -Test for acceleration: full coffee cup - if the coffee spills while driving, you are accelerating. -Calculation: a = (change in velocity or speed) / (change in time) - another way to write this is a = (vf - vi) / (t2 - t1) which we simplify to (vf - vi) / t Example: car speeds up from 10 m/s to 40 m/s over 5 seconds.
 * Change in V=30 m/s, change in T= 5 s**

4. Deceleration or negative acceleration
If an object slows down, the acceleration is negative (also called deceleration) In this class, all problems assume that acceleration is uniform - increasing or decreasing at a constant rate. - Calculation: distance traveled during acceleration = average speed * time - Average speed is (Vi + Vf) / 2 Take up acceleration problems using the three formulas given last class (the point is to solve problems using formulas that we already know). The kinematic equations will be used as well, but at this point they seem like a black box that mysteriously gives the correct answer. Introduce Kinematic equations - derive at least one - d = Vi t + 1/2 a t**²** - vf = vi + at - vf**²** = vi**²** + 2ad

5. Projectile Motion - primarily vertical and horizontal cases (we do the harder ones next year)
- for objects thrown vertically (either up or down), we define the upward direction and speed as positive and the downward direction and speed as negative. With projectiles, the acceleration from Earth's gravity is always negative. For example, a ball thrown upward, might have vi = 25 m/s, but that same ball will have an acceleration of (-) 9.8 m/s**².** If a ball is thrown downward, its initial speed might be (-)14 m/s, but its acceleration will still be (-) 9.8 m/s**²**. We need to make sure that our distance, speed, and acceleration values have directions associated with them - and the simplest is to identify UP as + and DOWN as -. - for objects thrown horiontally, we will find out that gravity pulls the same amount on an object travelling horizontally as on on object at rest. I will try to convince you that a dropped object will hit the floor at exactly the same time as an object thrown horizontally.