Kinematics – 1Dimensional Motion

Kinematics The branch of mechanics that describes the motion of objects without discussing what causes the motion 1-Dimensional Kinematics refers to motion in a straight line AP Physics B 1D Kinematics

Before describing motion, you must set up a coordinate system – define an origin and a positive direction You have the freedom to choose your coordinate system, but choose wisely. Keep it simple. AP Physics B 1D Kinematics

Important Terms to Know in Kinematics Position Distance Displacement Speed Velocity Acceleration Scalar Vector SI Units: meter second AP Physics B 1D Kinematics

Scalar and Vector Quantities All physical quantities will be either scalar or vector quantities. Scalar quantities are magnitudes – they describe how much Vector quantities are magnitudes and directions – they describe how much and in what direction (relative to your chosen coordinate system) AP Physics B 1D Kinematics

Distance Δx The total length traveled by an object. “How far have you walked?” is a typical distance question. It is a scalar quantity. The SI unit of distance is the meter (m). AP Physics B 1D Kinematics

The distance is the total length of travel; if you drive from your house to the grocery store and back, you have covered a distance of 8.6 mi. AP Physics B 1D Kinematics

Displacement (∆ 𝒙 ) The change in position of an object is called displacement. Δ is a Greek letter used to represent the words “change in”. ∆ 𝒙 therefore means “change in x”. It is a vector quantity – the arrow over the “x” indicates this. The SI unit is also the meter (m). Displacement is always calculated by final value minus initial value. ∆ 𝑥 =𝑥− 𝑥 0 AP Physics B 1D Kinematics

Displacement is the change in position Displacement is the change in position. If you drive from your house to the grocery store and then to your friend’s house, your displacement is 2.1 mi in the negative direction and the distance you have traveled is 10.7 mi. AP Physics B 1D Kinematics

Distance vs. Displacement Δx Scalar – magnitude only SI Unit: m Displacement ∆ 𝒙 Vector – magnitude and direction SI Unit: m B Displacement 50 m North Distance 100 m AP Physics B 1D Kinematics A

Practice Problem Two tennis players approach the net to congratulate each other after a game. Find the distance and displacement of player A. Repeat for player B. AP Physics B 1D Kinematics

Practice Problem If ∆ 𝒙 is the displacement of a particle, and Δx is the distance the particle traveled during that displacement, which of the following is always a true statement? Δx =|∆ 𝒙 | Δx<|∆ 𝒙| Δx >|∆ 𝒙 | Δx≥|∆ 𝒙 | Δx ≤|∆ 𝒙| AP Physics B 1D Kinematics

Practice Problem You are driving a car on a circular track of diameter 40 meters. After you have driven around 2 ½ times, how far have you driven, and what is your displacement? AP Physics B 1D Kinematics

Speed Speed describes how fast an object is moving. 𝑣= ∆𝑥 ∆𝑡 The SI unit of speed is m/s. Speed is always a positive number. AP Physics B 1D Kinematics

Velocity Velocity describes how fast the displacement is changing. 𝑣 = ∆ 𝑥 ∆𝑡 The SI unit is m/s. Velocity can be positive or negative depending on object’s direction AP Physics B 1D Kinematics

Average Velocity vs. Instantaneous Velocity Occasionally a problem will ask you to find the average velocity of an object. You are calculating the velocity of an object over a time interval ∆𝑡=𝑡− 𝑡 0 Other times a problem will ask you to find the instantaneous velocity. This is velocity at a single instant in time. If the velocity is constant, the instantaneous velocity is the same as the average velocity AP Physics B 1D Kinematics

This plot shows the average velocity being measured over shorter and shorter intervals. Eventually we reach the instantaneous velocity which is tangent to the curve. AP Physics B 1D Kinematics

Acceleration Any change in velocity over a period of time 𝑎 = ∆ 𝑣 ∆𝑡 2 𝑎 = ∆ 𝑣 ∆𝑡 2 SI unit: m/s2 Ways an object can be accelerating: Object changes speed Object changes direction Object change speed and direction AP Physics B 1D Kinematics

Sign of Acceleration Determining the sign of acceleration is a bit trickier than finding the sign of velocity General Rule: If the object is slowing down, acceleration has the opposite sign of it’s motion. Example: If the object is moving in the negative direction and slowing down, the acceleration is positive. AP Physics B 1D Kinematics

Is the car speeding up or slowing down? AP Physics B 1D Kinematics

Questions If acceleration is zero, what does this mean about the motion of the object? Is it possible for a racecar circling a track to have zero acceleration? AP Physics B 1D Kinematics

Kinematic Friends Learn and love these equations ∆𝑥= 𝑣 0 𝑡+ 1 2 𝑎 𝑡 2 𝑣= 𝑣 0 +𝑎𝑡 𝑣 2 = 𝑣 0 2 +2𝑎∆𝑥 AP Physics B 1D Kinematics

Practice Problem A plane is flying in a northwest direction when it lands, touching the end of the runway with a speed of 130 m/s. If the runway is 1.0 km long, what must the acceleration of the plane be if it is to stop while leaving ¼ of the runway remaining as a safety margin? AP Physics B 1D Kinematics

Practice Problem On a ride called the Detonator at Worlds of Fun in Kansas City, passengers accelerate straight downward from 0 to 20 m/s in 1.0 second. What is the acceleration of the passengers on this ride? How fast would they be going if they accelerated for an additional second at this rate? AP Physics B 1D Kinematics

Practice Problem You are driving through town at 12.0 m/s when suddenly a ball rolls out in front of you. You apply the brakes and accelerate at -3.5 m/s2. How far do you travel before stopping? When have you traveled only half the stopping distance, what is your speed? How long does it take you to stop? AP Physics B 1D Kinematics

Review The most useful tool to designate a simple and clear frame of reference in a physics problem is a: Vector magnitude Vector diagram Complete vector, with direction and magnitude Coordinate system Detailed written procedure AP Physics B 1D Kinematics

Review Displacement is a: Frame of reference Change in position of an object Vector magnitude Vector direction None of these AP Physics B 1D Kinematics

Review An object follows the path in the diagram. At the end of the motion what is the total distance traveled and the magnitude of the overall displacement? 11 km, 3 km 3 km, 11 km 11 km, 4 km 4 km, 11 km 11 km, 5 km AP Physics B 1D Kinematics

Review Under what conditions would average velocity and instantaneous velocity be equal? They are entirely different and this can never be true. Unlike speed, velocity has only one type so this is always true. When velocity changes at a uniform rate. This is consistently true when velocity is constant. Only when a change in direction occurs. AP Physics B 1D Kinematics

Review An object moving in a circular path completes one circumference. Which statement(s) below is (are) true? Displacement is zero Average speed is zero Velocity is changing Acceleration is zero I only I and II only I and III only IV only II and IV only AP Physics B 1D Kinematics

Review Which is not true of acceleration? Speed can be constant while accelerating. It is a change in velocity per unit of time. It is the rate of displacement. It can be either positive or negative. It can be a change in speed or direction. AP Physics B 1D Kinematics

Review Two objects starting at rest experience the same uniform acceleration. The second object accelerates for only half the time as the first object. How many times greater will the first object’s displacement be? ¼ ½ 1 2 4 AP Physics B 1D Kinematics

Review An object at the origin accelerates uniformly from rest. At the end of one second the object has displaced 10 m. What is the object’s speed after two seconds? 5 m/s 10 m/s 20 m/s 40 m/s 100 m/s AP Physics B 1D Kinematics

Review An object accelerates uniformly from rest reaching a final speed v after traveling at a set distance. If it continues to accelerate at the same rate, traveling to a point twice the original distance, it’s final speed will be Sqrt(2)v/2 Sqrt(2)v 2v 2sqrt(2)v 4v AP Physics B 1D Kinematics

Review A person moves at a constant 1.3 m/s for 2 hours. How far have they traveled? 9360 m AP Physics B 1D Kinematics

Review A car accelerates uniformly from a speed of 10.0 m/s to a speed of 20.0 m/s in a distance of 325 m. Determine the car’s acceleration 0.462 m/s2 Determine the time required for the acceleration 21.6 s AP Physics B 1D Kinematics

Review A bicyclist accelerates uniformly from rest to a speed of 12 m/s in a time of 30 s. Determine the bicyclist’s acceleration 0.40 m/s2 Determine the distance traveled during this time 180 m AP Physics B 1D Kinematics

Review An airplane, initially at rest, accelerates uniformly at 5.4 m/s2 down a runway that is 1.2 km long. What is the airplane’s speed when it reaches the end of the runway? 114 m/s How long does the airplane take to reach this speed? 21.1 s AP Physics B 1D Kinematics