Basic Kinematics PDF

Linear Motion  Vectors vs Scalars Scalars are quantities that have a magnitude, or numeric value which represents a size – Ex:14m or 76mph. Vectors are quantities which have a magnitude and a direction – Ex:12m to the right or 32mph east.  Describing how far you’ve...

Linear Motion  Vectors vs Scalars Scalars are quantities that have a magnitude, or numeric value which represents a size – Ex:14m or 76mph. Vectors are quantities which have a magnitude and a direction – Ex:12m to the right or 32mph east.  Describing how far you’ve gone Distanced DisplacementD Scalar Vector Standard units are Standard units are meters (m) meters (m) A measure of how far accompanied by you have moved with direction. respect to you (what a A measure of how far pedometer would you are with respect to measure) where you started (or change in position). Distance vs Displacement The person, according to a pedometer has walked a total of 12m. That is the distance traveled. The person walking stops where she started, so her displacement is zero.  Measuring how fast you are going SpeedS Velocityv Scalar Vector Standard unit is m/s Standard unit is m/s, plus direction distance d displacement D S  v  time t time t  Velocity and Speed If it take the person 4 For speed, d=12m seconds to walk around the square, what is her and t=4s, so v=3m/s average speed and For velocity, d=0 average velocity? and t=4s, so v=0m/s  Acceleration v v f  vi Change in velocity a  acceleration   t t over time. delta. Either hitting the gas or hitting the break Means “change in” counts as and is calculated by acceleration. subtracting the initial value from the final Units are m/s2 value. Using linear motion equations We always assume that acceleration is constant. We use vector quantities, not scalar quantities. We always use instantaneous velocities, not average velocities Direction of a vector is indicated by sign. Incorrect use of signs will result in incorrect answers.  Practice Problem A car going 15m/s accelerates at 5m/s2 for 3.8s. How fast is it going at the end of the acceleration? First step is identifying the variables in the equation and listing them.  Practice Problem A car going 15m/s accelerates at 5m/s2 for 3.8s. How fast is it going at the end of the acceleration? t=3.8s vi=15m/s a=5m/s2 vf=?  Practice Problem 2 A penguin slides down a glacier starting from rest, and accelerates at a rate of 7.6m/s2. If it reaches the bottom of the hill going 15m/s, how long does it take to get to the bottom?  Practice Problem 2 A penguin slides down a glacier starting from rest, and accelerates at a rate of 7.6m/s2. If it reaches the bottom of the hill going 15m/s, how long does it take to get to the bottom? Equation for displacement d v t d  vt v  1 vi  v f  2 d  1 vi  v f t 2  Practice Problems A car slows from 45 m/s to 30m/s over 6.2s. How far does it travel in that time? A cyclist speeds up from his 8.45m/s pace. As he accelerates, he goes 325m in 30s. What is his final velocity? Equation that doesn’t require vf d  1 vi  v f  t v f  vi  at 2 d  1 vi  vi  at t 2 d  1 t (2vi  at ) 2 d  vi t  at 1 2 2  Practice Problems A ball rolling up a hill accelerates at –5.6m/s2 for 6.3s. If it is rolling at 50m/s initially, how far has it rolled? If a car decelerates at a rate of –4.64m/s2 and it travels 162m in 3s, how fast was it going initially? An equation not needing t v f  vi  at d  1 vi  v f t 2 v f  vi  at  v f  vi  v f  vi t d 1 v  v f  2 i  a  a   v 2f  vi2  d1   2 a    2ad  v 2f  vi2  v  v  2ad 2 f 2 i A bowling ball is thrown at a speed of 6.8m/s. By the time it hits the pins 63m away, it is going 5.2m/s. What is the acceleration?  The Big 4 v f  vi  at v  v  2ad 2 f 2 i d 1 2 at  vi t 2 d  1 vi  v f t 2  Gravity Gravity causes an acceleration. All objects have the same acceleration due to gravity. Differences in falling speed/acceleration are due to air resistance, not differences in gravity. g=-9.8m/s2 When analyzing a falling object, consider final velocity before the object hits the grounds.  Problem Solving Steps Identify givens in a problem and write them down. Determine what is being asked for and write down with a questions mark. Select an equation that uses the variables (known and unknown) you are dealing with and nothing else. Solve the selected equation for the unknown. Fill in the known values and solve equation  Hidden Variables Objects falling through space can be assumed to accelerate at a rate of –9.8m/s2. Starting from rest corresponds to a vi=0 A change in direction indicates that at some point v=0. Dropped objects have no initial velocity.  Practice Problem A ball is thrown upward at a speed of 5m/s. How far has it traveled when it reaches the top of its path and how long does it take to get there? vi=5m/s d=? vf=0m/s t=? a=g=-9.8m/s2 A plane slows on a runway from 207km/hr to 35km/hr in about 527m. a. What is its acceleration? b. How long does it take? An onion falls off an 84m high cliff. How long does it take him to hit the ground? An onion is thrown off of the same cliff at 9.5m/s straight up. How long does it take him to hit the ground? A train engineer notices a cow on the track when he is going 40.7m/s. If he can decelerate at a rate of -1.4m/s2 and the cow is 500m away, will he be able to stop in time to avoid hitting the cow?  Displacement (Position) vs. Time Graphs Position, or displacement can be determined simply by reading the graph. What is the velocity of the Velocity is determined by object at 4 seconds? the slope of the graph (slope equation will give units of m/s). If looking for a slope at a specific point (i.e. 4s) determine the slope of the entire line pointing in the same direction. That will be the same as the slope of a specific point.  Velocity vs. Time Graphs Velocity is determined by reading the graph. Acceleration is determined by reading the slope of the graph (slope equation will give units of m/s2).  Velocity vs. Time Graphs Displacement is found using area between the curve and the x axis. This area is referred to as the area under the curve (finding area will yield units of m). Areas above the x axis are considered positive. Those underneath the x axis are considered negative. Break areas into triangles (A=1/2bh), rectangles (A=bh), and trapezoids (A=1/2[b1+ b2]h).  Velocity vs. Time Graphs What is the acceleration of the object at 6s? What is the displacement of the object at 4s? What is the displacement of the object from 3s to 12s?