Description of Motion

Description of Motion: Speed, Velocity, Acceleration Speed is a scalar quantity which refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. A fastmoving object has a high speed and covers a relatively large distance in a short amount of time. A slow-moving object has a low speed and covers a relatively small amount of distance in a short amount of time. An object with no movement at all has a zero speed. Velocity is a vector quantity which refers to "the rate at which an object changes its position." Imagine a person moving rapidly - one step forward and one step back always returning to the original starting position. While this might result in a frenzy of activity, it would result in a zero velocity. •

•

Speed is the rate of motion, or the rate of change of position. It is expressed as distance moved (d) per unit of time (t). Speed is a scalar quantity with dimensions distance/time. Speed is measured in the same physical units of measurement as velocity, but does not contain an element of direction. Speed is thus the magnitude component of velocity. Velocity contains both the magnitude and direction components. Calculating Average Speed and Average Velocity The average speed during the course of a motion is often computed using the following formula:

Meanwhile, the average velocity is often computed using the equation

Acceleration Acceleration, (symbol: a) is defined as the rate of change of velocity. It is thus a vector quantity with dimension length/time². In SI units, acceleration is measured in meters/second². To accelerate an object is to change its velocity, which is accomplished by altering either its speed or direction (like in case of uniform circular motion) in relation to time. Acceleration can have positive and negative values. Any time that the sign (+ or -) of the acceleration is the same as the sign of the velocity, the object will speed up. If the signs are opposite, the object will slow down. Acceleration is a vector quantity. When either velocity or direction changes, there is acceleration (or deceleration). To accelerate an object requires the application of a force. Acceleration is the rate at which velocity is changing with respect to time (m/s/s or m/s2).  An object accelerates when its speed is increasing, when its speed is decreasing and/or when its direction is changing. a = (vf − vi)/(tf − ti) (m/s2) where:

vf − vi is the final velocity minus the initial velocity

tf − ti is the measured time period between the two velocities Often this is written as a = Δv/Δt, where Δ is the Greek letter delta and stands for difference. Calculating the Average Acceleration The average acceleration (a) of any object over a given interval of time (t) can be calculated using the equation

This equation can be used to calculate the acceleration of the object whose motion is depicted by the velocity-time data table above. The velocity-time data in the table shows that the object has an acceleration of 10 m/s/s. The calculation is shown below.

Uniform Accelerated Motion Equations

a.) a =

v f − vi t

b.) d = Vi t +

1 2 at 2

2

2

c.) V f = Vi + 2 a d

Drills: 1. Calculate the average speed (in km/h) of JoJo, who runs to the store 6 kilometers away in 45 minutes. 2. Calculate the distance (in km) that JoJo runs if he maintains his average speed for 1.5 hour. 3. Starting from rest, both going in a straight horizontal line, one car accelerates to a speed of 30 km/h, and another car accelerates to a speed of 20 km/h. Can you say which car underwent the greater acceleration? Why or why not? (2 points). Show your work and justify your answer.

Drill: UAM Problems 1.) What is the displacement of a train as it is accelerated uniformly from + 11 m/s to + 33 m/s in a 20.0 s interval? 2.) A race car traveling at 44 m/s is uniformly accelerated to a velocity of 22 m/s over an 11 second interval. What is its displacement during this time? 3.) A bike rider accelerates constantly to a velocity of 7.5 m/s during 4.5 s. The bike’s

displacement is 19 m. What was the initial velocity of the bike? 4.) A car accelerates at a constant rate from 15 m/s to 25 m/s while it travels 125 m. How long does this motion take? 5.) A rocket traveling at 88 m/s is accelerated uniformity to 132 m/s over a 15 second interval. What is its displacement during this time? 6.) A car starting from rest accelerates uniformly at 6.1 m/s2 for 7.0 s. How far does the car move? 7.) An airplane starts from rest and accelerates at a constant + 3.00 m/s2 for 30 s before leaving the ground. What is its displacement during this time? 8.) Starting from rest, a race car moves 110 m in the first 5.0 s of uniform acceleration. What is the car’s acceleration? 9.) A driver brings a car traveling at 22 m/s to a full stop in 2.0 s. Assume its acceleration is constant. A.) What is the car’s acceleration? B.) How far does it travel before stopping? 10.) A biker passes a lamppost at the crest of a hill at + 4.5 m/s. She accelerates down hill at a constant rate of 0.40 m/s2 for 12 s. How far does she move down the hill during this time?

MOTION PROBLEMS (Speed, Velocity, P – T Graph, V – T graph) A. Description of Motion/ Velocity/Acceleration

Speed/

Velocity/

Average

Speed/

Average

1. What must be your car’s average speed (m/s) in order to travel 235 km in 3.25 hr? 2. A car travels a distance of 40 km from Manila to a town in Laguna. What is its average speed (in km/hr) if travelling time is from 7:00 am to 7:30 am? Average velocity in km/hr? Suppose that after a business talk with a friend, the driver of the car drives straight back to Manila from 11:55 am to 12:20 pm. What was the car’s average speed (in km/hr) during the round trip? Average velocity in km/hr? 3. A rolling ball moves from x1 = 3.4 cm to x2 = – 4.2 cm during the time from t 1 = 3.0 s to t2 = 6.1 s. What is its average velocity in m/s? 4. An airplane flies eastward through still air with a velocity of 185 km/hr. Suddenly a tail wind blows with a velocity of 9 km/hr eastward. What is the resultant velocity of the airplane? 5. Which has greater deceleration, a bicycle slowing from 3 m/s to a stop in 6 seconds or a car slowing from 20 m/s to 15 m/s in 6 second? 6. A skater moving at 5 m/s begins to decelerate at 1 m/s each second. How fast will it be moving after 4 seconds? 7. A truck’s velocity on a straight high way increases uniformly from 15 km/hr to 60 km/hr in 20 s. Determine: a. the average speed in km/hr and m/s; b. the acceleration in m/s2; c. the distance travelled during this period 8. A bus travelling 50 m/s is increasing its speed at the rate of 4 m/s 2. a. Find the distance covered in 6 s; b. If its speed is decreasing at the rate of 4 m/s2, find the distance covered in 6 s and the time it takes to come to rest. 9. A cannon barrel is 6 m long. The muzzle velocity of a bullet from the cannon is 305 m/s. What is the average acceleration of the bullet through the barrel? 10. A sports car accelerates from rest to 95 km/hr in 6.2 s. What is its average acceleration in m/s2? 11. A person jogs eight complete laps around a quarter mile track in a total time of 12.5 min. Calculate (a) the average speed in m/s and (b) the average velocity in m/s. 12. Two locomotives approach each other on parallel tracks. Each has a speed of 95 km/hr with respect to the ground. If they are initially 8.5 km apart, how long will it be before they reach each other? 13. A sports car moving at constant speed travels 110 m in 5.0 s. If it then brakes and comes to a stop in 4.0 s, what is its acceleration in m/s2? B. Position-time Graph/ Velocity-time Graph 14. The following data were obtained for the position of a ball as it rolled along a straight track. Plot these data and determine the average velocity of the ball during this time interval. Was the velocity constant?

Displacement (cm) 2.90 7.40 11.00 22.70 31.10

Time (s) 0.60 2.10 3.30 7.20 10.00

15. The tabulated data show the displacement of a car against time. The distance and the time are both taken to be zero at the beginning of the motion. a. Plot d against t b. What kind of displacementtime relation is shown by your graph?

Displacement (cm) 3.81 14.2 32.0 57.9 91.4

Time (s) 2 4 6 8 10

c. What is the velocity of the car at t = 3.5 s

These graphs show various relationship of velocity v of a body to time t and displacement d. Which graph represents the following conditions? 16. Uniform motion 17. uniform acceleration 18. increasing velocity 19. no motion 20. decreasing velocity

21. This position-time graph shows the motion of a delivery truck whose driver is trying to find a certain house on a long straight street.

a) b) c) d) e)

What is the truck’s position at 15 s? at 50 sec? What is the truck’s velocity at intervals A, B, and C? What is the displacement between 0 to 30 sec? What is the total distance traveled for the first 30 sec? What is the total distance of the entire trip?

22. Odina walked down the hall at school from the canteen to the PEHM faculty room, a distance of 100.0 m. A class of physics students recorded and graphed her position every 2.0 s noting that she moved 2.6 m every 2.0 s. When was Odina in the following positions: a. 25.0 m from the canteen b. 25.0 m from the PEHM faculty room c. Create a graph showing Odina’s motion. 23. Analysis of v-t graph:

Guide Questions: 1. Calculate the Acceleration at each interval: a. t = 0 s to t = 4 s b. t = 2 s to t = 4 s c. t = 4 s to t = 10 s d. t = 10 s to t = 12 s e. t = 12 s to t = 14 s f. t = 14 s to t = 16 s 2. Calculate the average acceleration for the entire trip. 3. Calculate the average acceleration from t = 0 s to t = 10 s. 4. Calculate the average acceleration during the last four intervals. 5. Calculate the distance travelled at each interval (a – f). 6. Calculate the total distance travelled for the entire trip. 7. Calculate the distance travelled from t = 0 s to t = 12 s. 8. Calculate the distance travelled during the last three intervals. 9. What interval the cart travels the shortest distance? 10. What interval the cart attained the greatest acceleration? 11. How many intervals the acceleration equal to zero.

PRE TEST – Speed, Velocity, Acceleration, UAM A. Multiple Choice. 1. Which of the following choices describe the car’s motion?

a.) b.) c.) d.)

negative velocity, negative acceleration negative velocity, positive acceleration positive velocity, negative acceleration positive velocity, positive acceleration

2. The units for acceleration are: a.) m/s b.) m/s2

c.) second d.) (m/s)2

3. Which of the following is/are true about acceleration? a.) Acceleration is a change in velocity b.) An applied force is required for acceleration to occur c.) Acceleration can be either + or - in value. d.) All of the above 4. Which of the following choices describe the car’s motion?

a.) b.) c.) d.)

negative velocity, moving to the left negative velocity, moving to the right positive velocity, moving to the left positive velocity, moving to the right

5. If a car going in a straight line increases its velocity from zero to 100 km/h in 35 seconds, its average acceleration is a.) 2.86 km/h/s c.) actually, the same as the acceleration of free fall b.) 3.72 km/h/s d.) two of these 6. A football coach paces back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D.

What is the coach's average speed and average velocity? a.) 9.5 yd/min, 5.5 yd/min (left) c.) 5.5 yd/min, 5.5 yd/min (right) b.) 5.5 yd/min, 9.5 yd/min (right) d.) too little information, can’t be solved 7. A car going at 15 m/s undergoes an acceleration of 2 m/s2 for 4 seconds. What is its final speed? a.) 38 m/s c.) 27 m/s b.) 23 m/s d.) 2 m/s 8. If positive acceleration occurs in the same direction as an object’s velocity, then that object is __________________. a.) in constant motion c.) slowing down b.) speeding up d.) moving at a uniform rate For numbers 9 and 10: Consider the following problems and the corresponding solutions. Use the equation for acceleration to determine the acceleration for the following two motions.

9. What is the acceleration in Practice A? 10. What is the acceleration in Practice B? B. Problem Solving

1. How long does it take for a car to change its velocity from 10 m/s to 25 m/s if the acceleration is 5 m/s2? 2. A rat and a cat is 35 m apart. When the rat started to run at 2 km/h (0.556 m/s), the cat started to chase him at 1 m/s2. Can the cat catch the rat in 10 seconds? 3. A car has a constant acceleration of 4 m/s2, starting from rest. a. How fast is it traveling after 5 seconds? b. b. How far is it traveling after 5 seconds? c. How far has it traveled by the time it reached the speed of 40 m/s?