Displacement, Velocity, and Acceleration AP style

Displacement, Velocity, and Acceleration AP style

Linear Motion Position- the location of an object relative to a reference point. IF the position is one-dimension only, we often use the letter x to represent position. If, however, if the position is two or three dimensions, r is generally used. For example, position, x = 4.2 m or perhaps r = 4.2 m East + 6.7 m North. Reference point- the point from which measurements are made.

Relative Motion All motion is RELATIVE. The position and velocity of an object depend on the reference point.

Relative Motion When your car has a constant velocity, how fast it is going is determined by WHO is doing the measuring: a car passing you, a car approaching you, the policeman beside the road, OR you, yourself.

According to YOUR frame of reference, your car is sitting perfectly still and the countryside is moving backwards! Relative Motion

For instance, how fast are you moving right now??? According to you or. According to a Martian

Distance- how far something moves. Displacement change in position, Dx = x x o how far something moves in a given direction. (It s only concerned about where you started and where you stopped, not what you did in between.) For example: if you take a trip all the way around the world and end up right back where you started, you traveled a great distance, but your displacement was zero!

Speed and Velocity In physics, speed and velocity are not the same! Speed is how fast, Velocity is how fast and in what direction. Example: 10 m/s is a speed, 10 m/s north is a velocity

Vectors: quantities that have both magnitude and direction Velocity is a vector Speed is a SCALAR- it has only magnitude. You may have a negative velocity, but there is no negative speed.

How to calculate speed and velocity speed = distance time velocity = displacement time

Instantaneous velocity- the velocity at any instant Average speed = total distance covered time interval Average velocity = Total displacement time interval

D - delta - a symbol that means the change in D x = the change in position Change in time, D t Change in velocity, D v The change in a value is the difference between the final value and the original value- final minus original D velocity = final velocity original velocity

uniform means constant, unchanging At a uniform speed, the distance traveled is given by Distance = speed x time At uniform velocity, the displacement is given by Displacement = velocity x time d = Dx = vt (Remember, displacement = Dx = x x o )

Calculus Connection Remember, the average velocity is given by Δx Δy or Δt Δt Whereas, the instantaneous velocity is given by the derivative of position.. dx dy or dt dt Graphically, the instantaneous velocity is the Slope of the tangent line to the position curve.

Graphing Motion The velocity of an object can be found by determining the SLOPE on a position-time graph.

Slope =??? Slope =??? What about the DIRECTION of the instantaneous displacement and instantaneous velocity (BOTH are VECTORS!) at t = 5s?

Velocity-Time Graphs Velocity (m/s) 8 6 What is the velocity? At 1 s? At 4 s? At 7 s? At 12 s? At 17 s? What is the acceleration? From 0 2s? From 2 6 s? From 9 11 s? From 11-14 s? From 14 22 s? 4 2-2 -4-6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Time (s) The ACCELERATION is found by taking the SLOPE of the velocity vs. time graph -8

Velocity-Time Graphs Velocity (m/s) 8 6 What is the velocity? At 1 s? 6m/s At 4 s? 3m/s At 7 s? 0 At 12 s? -8m/s At 17 s? -4m/s What is the acceleration? From 0 2s? 0 From 2 6 s? -1.5 m/s 2 From 9 11 s? -4m/s 2 From 11-14 s? 0 From 14 22 s? +1.4m/s 2 4 2 What about the displacement? Displacement from the starting point = the area of the shapes. Shapes below the x- axis will be negative displacement! -2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Time (s) -4-6 -8

Acceleration Acceleration: the rate at which velocity changes Acceleration = final Δ velocity time velocity - original time velocity Unit: Δ velocity time m/s s m 2 s accelerated motion applet

Calculus Connection Remember, the average acceleration is given by Dv/Dt Whereas, the instantaneous acceleration is given by dv/dt Graphically, the instantaneous acceleration is the Slope of the tangent line to the velocity curve

Remember, velocity is how fast (speed) AND in what direction. If either speed OR direction changes, the velocity has changed, which means that there is an acceleration!

How to tell if you accelerated too quickly.

Constant velocity means that neither the speed nor the direction of motion can change. ball on string applet A race car driving around a circular path at a constant 80 mi/h has a constant speed but not a constant velocity since its direction is changing.

So An object accelerates when its speed OR its direction changes!

Positive or Negative? Choose a direction for + and then stick with it! Going forward, speeding up Going forward, slowing down Going backward, speeding up Going backward, slowing down Velocity pos pos neg neg Acceleration pos neg neg pos

Free Fall: the movement of an object in response to a gravitational attraction Earth s gravity, ignoring air resistance, produces an acceleration of we often just call g, the acceleration due to gravity. The size of g is 9.8 m/s 2, but since the acceleration vector is always directed downward, the value of the acceleration is a = - g = - 9.8 m/s 2 (approximately -10 m/s 2 ) But. Sometimes, we choose downward to be the positive direction, in which case, a = +9.8 m/s 2.

What does this mean? Each second of free-fall, the speed of an object increases by about 10 m/s T = 1s Speed = 10 m/s T = 2s Speed = 20 m/s T = 3s Speed = 30 m/s

v O = original velocity v = final velocity KEY WORDS stops The final velocity is zero, v = 0 at rest The original velocity is zero, v o = 0 dropped falling freely

Positive or Negative? Up= positive Down = Negative If you throw a ball upward, As it moves upward, its velocity is positive. As it falls back down, its velocity is negative. At the highest position, its velocity is ZERO.

What about the sign of acceleration? On the way up, its acceleration is negative. On the way down, its acceleration is negative. At the highest point, its acceleration is negative. The acceleration is ALWAYS negative! It s always -9.8 m/s 2 because the acceleration is due to CONSTANT gravity!

MORE KEY WORDS dropped : v o = 0, a = -9.8 m/s 2 (-10 m/s 2 ) reaches its highest point : velocity = 0 In ALL free fall problems, the acceleration, assuming downward is negative, is always a = - 9.8 m/s 2 Remember, you need to find THREE numbers to be able to solve for the fourth quantity.

What s the speed? 10 m/s 0 m/s 10 m/s 20 m/s 20 m/s 30 m/s 30 m/s

If the ball was thrown upward with a velocity of 50 m/s, how long would it take to reach its highest point? What if the original velocity was 70 m/s? 35 m/s? Does the ball travel the same distance during each second?

If the ball was thrown upward with a velocity of 50 m/s, how long would it take to reach its highest point? What if the original velocity was 70 m/s? 35 m/s? Does the ball travel the same distance during each second?

Remember, how fast is NOT the same as how far A bird egg falls out of a nest high in a tree. How FAST is it moving in 1 second? V o = 0 a = -10 m/s 2 t = 1s v f =? V f = v o + at V f = 0 + -10(1) = -10 m/s How FAR will it fall in 1 second? D = v o t + ½ at 2 D = 0 + ½ (-10) 1 2 D = - 5 m (distance is +5 m)

If the object was thrown upward or downward, not DROPPED, then the original velocity would not equal zero. An ant takes a ride on a helium balloon as it moves upward. If the ant lets go when the balloon is moving at a constant speed of 20 m/s upward, What is the ant s velocity in 5 seconds? v f = v o + at How far below the balloon is the ant in 5 seconds? d = v o t + ½ at 2 Be careful, the balloon continues to move upward at a constant 20 m/s!