Presentation on theme: "One Dimensional Motion"— Presentation transcript:
1 One Dimensional Motion Section 1 Displacement and VelocityChapter 2One Dimensional MotionTo simplify the concept of motion, we will first consider motion that takes place in one direction.One example is the motion of a commuter train on a straight track.To measure motion, you must choose a frame of reference. A frame of reference is a system for specifying the precise location of objects in space and time.
2 displacement = final position – initial position Section 1 Displacement and VelocityChapter 2DisplacementDisplacement is a change in position.Displacement is not always equal to the distance traveled.The SI unit of displacement is the meter, m.Dx = xf – xidisplacement = final position – initial position
3 Positive and Negative Displacements Section 1 Displacement and VelocityChapter 2Positive and Negative Displacements
4 Chapter 2 Average Velocity Section 1 Displacement and VelocityChapter 2Average VelocityAverage velocity is the total displacement divided by the time interval during which the displacement occurred.In SI, the unit of velocity is meters per second, abbreviated as m/s.
5 Chapter 2 Velocity and Speed Section 1 Displacement and VelocityChapter 2Velocity and SpeedVelocity describes motion with both a direction and a numerical value (a magnitude).Speed has no direction, only magnitude.Average speed is equal to the total distance traveled divided by the time interval.
6 Interpreting Velocity Graphically Section 1 Displacement and VelocityChapter 2Interpreting Velocity GraphicallyFor any position-time graph, we can determine the average velocity by drawing a straight line between any two points on the graph.If the velocity is constant, the graph of position versus time is a straight line. The slope indicates the velocity.Object 1: positive slope = positive velocityObject 2: zero slope= zero velocityObject 3: negative slope = negative velocity
7 Interpreting Velocity Graphically, continued Section 1 Displacement and VelocityChapter 2Interpreting Velocity Graphically, continuedThe instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path.The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.
8 Chapter 2 Changes in Velocity Section 2 AccelerationChanges in VelocityAcceleration is the rate at which velocity changes over time.An object accelerates if its speed, direction, or both change.Acceleration has direction and magnitude. Thus, acceleration is a vector quantity.
9 Changes in Velocity, continued Chapter 2Section 2 AccelerationChanges in Velocity, continuedConsider a train moving to the right, so that the displacement and the velocity are positive.The slope of the velocity-time graph is the average acceleration.When the velocity in the positive direction is increasing, the acceleration is positive, as at A.When the velocity is constant, there is no acceleration, as at B.When the velocity in the positive direction is decreasing, the acceleration is negative, as at C.
10 Relationship Between Acceleration and Velocity Chapter 2Relationship Between Acceleration and VelocityUniform velocity (shown by red arrows maintaining the same size)Acceleration equals zero
11 Relationship Between Velocity and Acceleration Chapter 2Relationship Between Velocity and AccelerationVelocity and acceleration are in the same directionAcceleration is uniform (blue arrows maintain the same length)Velocity is increasing (red arrows are getting longer)
12 Relationship Between Velocity and Acceleration Chapter 2Relationship Between Velocity and AccelerationAcceleration and velocity are in opposite directionsAcceleration is uniform (blue arrows maintain the same length)Velocity is decreasing (red arrows are getting shorter)
13 Kinematic Equationsa = Δ v = vf - vi ti = 0Δ t tf - tiThereforevf = vi at
14 Kinematic Equations Vavg = Δx t Δx = vavgt = vi + vf t 2 Δx = ½ (vi + vf) tBut vf = vi atΔx = ½ (vi + vi at) tΔx = vi t + ½ at2
15 Kinematic Equations Δx = ½ (vi + vf) t We can develop an equation without tvf = vi att = vf - vi (sub. into equation above for ΔX)avf2 = vi aΔx
16 x a 2 v at 1 t D + = ÷ ø ö ç è æ Kinematic Equations Summary Uniform Acceleration equations of motionxa2vat1tifaverageD+=÷øöçèæ
17 Velocity and Acceleration Chapter 2Section 2 AccelerationVelocity and Acceleration
18 Free FallAll objects moving under the influence of only gravity are said to be in free fallAll objects falling near the earth’s surface fall with a constant accelerationGalileo originated our present ideas about free fall from his inclined planesThe acceleration is called the acceleration due to gravity, and indicated by g
19 Acceleration due to Gravity Free FallAcceleration due to GravitySymbolized by gg = 9.8 m/s²g is always directed downwardtoward the center of the earth
20 Free Fall -- an object dropped Initial velocity is zeroLet up be positiveUse the kinematic equationsGenerally use y instead of x since verticalvi= 0a = g
21 Free Fall – an object thrown downward a = gInitial velocity 0With upward being positive, initial velocity will be negative
22 Free Fall – object thrown upward Initial velocity is upward, so positiveThe instantaneous velocity at the maximum height is zeroa = g everywhere in the motiong is always downward, negativev = 0