PHYS 100 Chapter Notes - Chapter 2: Coordinate System, One Direction, International System Of Units
10 May 2018
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Chapter 2
Introduction to One Dimensional Kinematics
- Kinematics is defined as the study of motion without considering its causes.
Displacement
- Position
o In order to describe the motion of an object you must be able to describe its position
▪ Where it is at any particular time
▪ Specify its position relative to a convenient reference grame
- Displacement (SI Unit is the Meter)
o If an object moves relative to a reference frame then the objecys position changes
o This change in position is known as displacement
▪ It implies that an object has been moved or “displaced”
o Δ x = xf−x0
▪ Example: Professor paces left and right, starting at 1.5m and ending at 3.5m,
what is the displacement?
• 3.5-1.5 = +2m
o Displacement has a direction as well as a magnitude.
- Distance
o Defined to be the magnitude or the size of displacement between two positions
o Distance traveled is the total length of the path travelled between two position
▪ No direction and thus no sign
• Example: a cyclist rides 3km west and turns around and rides 2km east
o What is a) Displacement
• Δ x = xf−x0
o 2-3 = -1km
▪ B) Distnace
• 2km+3kn = 5km
▪ C) Magnitude
• 1km
Vectors, Scalars, Coordinate Systems
- Vector
o A vector is any quantity with both magnitude and direction
▪ Example includes: 90km/hour east
• Force of 500 newtons Straight down
o Direction of a vector in one dimensional motion is given by a + or a – sign
o Represented by arrows, which are used to represent a vector has a length proportional to
vectors magnitude
o Coordinate system
▪ You must designate a coordinate system to describe the direction of a vector
quantity
• Motion of right is +x, Left is -x, Upwards is +y and down is -y
Time Velocity Speed
- Time (SI Unit is the second)
o Time is change, or the interval over which change occurs
o The amount of time or change is calibrated by comparison with a standard
find more resources at oneclass.com
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o Δ t =tf−t0
▪ Δt is the change in time
▪ Tf is the time at the end of the motion
▪ T0 is the initial time
• Motion starts time equal to zero
- Velocity
o Has units of distance by time, miles per hour or kilometers per hour
▪ Calculated as displacement divided by time of travel
• v - = Δx/Δt = xf−x0/tf−t0
▪ Example: An airplane passenger took 5 seconds to move -4m
• -4m/5s = -0.8m/s
o Negative indicates that the person is going to the left
o Instant velocity is the average velocity at a specific instant in time
- Speed
o Speed is a scalar and has no direction
o Instantaneous speed is the magnitude of instantaneous velocity
o Average speed is the distance traveled divided by elapsed time
▪ Example: A train travels from Baltimore to DC in 1hr 45mins. The distance
between the two stations is 40miles.
• What is a) Average velocity
▪ Xf = x0 because it returns back
o B) Average speed
▪ Distance/time
• 80/105mins
• 80miles/105minutes x 5280 feet/1mile x 1
meter/3.28 feet x 1 minute/60 seconds = 20m/s
Acceleration
- The greater the acceleration, the greater the change in velocity over a given time
o Rate at which velocity changes
o A = Δv/Δt = vf −v0/tf−t0
- SI Unit is M/s2
o How many meters per second the velocity changes every second
o Change in velocity can be a change in magnitude, but can also be a change in direction
▪ Acceleration can change either in magnitude or direction
▪ A change in either speed or direction or both
o Acceleration is opposite to the direction of its motion, it is Deceleration
▪ Example: A car accelerates from rest to a velocity of 15m/s in 1.8s
• What is average acceleration
o Vf-V0/tf-t0
▪ (-15m/s)/1.8s = -8.33m/s2
- Instantaneous Acceleration
o Acceleration at a specific instant in time
- Examples
o Calculate Average velocity
▪ Xf = 3.75km
▪ X0 = 5.25km
▪ Δt = 5min
• 3.75km-5.25km/5min
• -1.5/5min*60min/1hr = -18.0km/hr
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Kinematics is defined as the study of motion without considering its causes. In order to describe the motion of an object you must be able to describe its position: where it is at any particular time, specify its position relative to a convenient reference grame. If an object moves relative to a reference frame then the objecys position changes: this change in position is known as displacement. Instant velocity is the average velocity at a specific instant in time: negative indicates that the person is going to the left. Speed: speed is a scalar and has no direction. Instantaneous speed is the magnitude of instantaneous velocity: average speed is the distance traveled divided by elapsed time, example: a train travels from baltimore to dc in 1hr 45mins. The greater the acceleration, the greater the change in velocity over a given time: rate at which velocity changes, a = v/ t = vf v0/tf t0.
