1. 1 Physics Chapter 2 Motion in One Dimension Topics:Displacement & Velocity Acceleration Falling Objects

2. 2 Displacement Displacement – change in position This measurement contains a magnitude & a direction (vector quantity) Distance traveled is different, though both are linear measurements Displacement (in 1 dimension) can be + (up or right) or – (down or left). What does a negative displacement indicate?

3. 3 Velocity Displacement per unit time = velocity v = x f – x i / t f - t i This provides average velocity Vector quantity (has magnitude & direction) When graphed (t = x, d = y), the slope of the line represents average velocity Instantaneous velocity would be the tangent of the slope at any point along the graph What does a negative velocity indicate?

4. 4 Acceleration Acceleration = Δ velocity per unit time A = v f – v i / t f - t i Vector quantity (has magnitude & direction) When graphed, the line shows the motion of the object over time Increasing speed is indicated by an upward slope Decreasing speed is indicated by a downward slope Constant speed is indicated by a straight line (no slope)

5. 5 Motion with Constant Acceleration Motion with constant acceleration will show an object’s velocity increasing by the same amount during each time interval & displacement increases by the same amount during each time interval Displacement with constant acceleration d = ½ (v i + v f ) Δt Example: Race car reaches speed of 42m/s; begins a uniform negative acceleration using a parachute and brake, and comes to rest 5.5s later. How far did the car move while stopping?

6. 6 More acceleration equations Velocity with constant acceleration V f = v i + a Δt Displacement with constant acceleration d = v i Δt + ½ a( Δt) 2 Example: A plane starting at rest at one end of a runway undergoes a constant acceleration of 4.8m/s 2 for 15s before takeoff. What is its initial speed at takeoff? How long must the runway be for the plane to takeoff?

7. 7 More acceleration equations To find final velocity without knowing time, use this equation Final velocity after any displacement v f 2 = v i 2 + 2a Δd The square root of the right side of equation to find final velocity, so be careful with determining the direction of motion Look at sample problem 2E pg 57 in text

8. 8 Falling Objects Objects in free fall undergo constant acceleration due to gravity Mass does not matter Air resistance (force acting against gravity) does impact objects in free fall Look at ball in free fall; note displacement between time intervals is not same, so velocity is not same, ball is accelerating.

9. 9 Acceleration Free fall acceleration is denoted by symbol “g” At Earth’s surface g = 9.8m/s 2 or 32 ft/s 2 Acceleration is due to gravity, thus objects accelerate towards the center of Earth and since it is in a down direction, for objects in free fall a = -g = - 9.8m/s 2 Be careful, though velocity is changing with time, acceleration due to gravity is constant

10. 10 What goes up, must come down… If a ball is thrown upward, it will have an initial velocity imparted to it by the thrower The ball will also have a constant acceleration of -9.8m/s 2 during the upward ascent Realize that the ball will slow down by 9.8m/s for each s it is ascending The ball will reach a point at which it changes direction (at the apex of the throw) and returns to Earth, at this point v = 0 m/s, but a = -9.8 m/s 2 all along the path As the ball falls, its velocity will increase by 9.8 m/s for each s of fall while maintaining an a = -9.8m/s 2 Look at page 61, Figures 2.14 & 2.15.

11. 11 Some things to remember …. Freely falling objects have same downward acceleration Downward acceleration is the same when object is moving up, stopped at top of path, or moving down The only thing changing is the magnitude and direction of velocity When an object is going up: a = negative, v = positive (the object is slowing down) An object is at rest at top of throw: a = negative, v = zero (for that instant direction is changing) When an object is going down: a = negative, v = negative (the object is speeding up)

12. 12 Problems: Practice 2D Q1-4, page 55 Practice 2E Q1-5, page 58 Section Review Q1-6, page 59 Practice 2F Q1-6, page 64 Section Review Q1-6, page 65 Chapter Review Q1-12,15, 18-19, 22-29, pages 69-71 DUE: Friday 9/17/10