Chapter 2: Kinematics Textbook Notes

• Kinematics


  The study of motion without considering its cause
• Position


  Where an object is at any particular time
• Displacement


  A change in an object's position.
• Displacement equation

  delta x = x_f - x_0
• delta x


  Displacement
• x_f


  Final position
• x_0


  Initial position
• delta


  Change in
• Distance

  The magnitude or size of displacement between two positions
• Distance traveled

  The total length of the path traveled between two positions
• A cyclist rides 3 km west and then turns around and rides 2 km east. a) What is their displacement? b) What distance do they ride? c) What is the magnitude of their displacement?

  a.) -1 km, b) 5 km, c) 1 km
• Vector


  Any quantity with both magnitude and direction. Its direction in one dimensional models is represented by a plus or minus sign. They are represented graphically by arrows, where the length is proportional to the magnitude and points in the same direction. Ex: displacement
• Scalar


  Any quantity hat has a magnitude but no direction. They are never represented by arrows. Ex: Distance
• A person's speed can stay the same as they round a corner and change direction. Given this information, is speed a scalar or vector quantity? Explain

  Speed is a scalar quality because it does not change at all with direction changes; therefore, it has magnitude only.
• Time


  Change, or the interval over which change occurs
• Elapsed time, or delta t


  The difference between the ending time and beginning time
• Equation for elapsed time

  delta t = t_f - t_0
• t_f


  Time at the end of motion
• t_0


  Time at the beginning of motion
• Average velocity

  The displacement divided by the time of travel
• Average velocity equation

  average velocity = delta x / t
• SI unit for velocity

  m/s
• Instantaneous velocity or v


  The average velocity at a specific instant in time. Ex: The number on a car's speedometer
• Instantaneous speed


  The magnitude of instantaneous velocity
• Average speed

  The distance traveled divided by elapsed time
• A commuter train travels from Baltimore to Washington DC and back in 1 hour and 45 minutes. The distance between the two stations is approximately 40 miles. What is a) the average velocity of the train, and b) the average speed of the train in m/s?

  a.) 0 because x_f = x_0. b) 20 m/s
• Acceleration

  Change in speed or direction, or both
• Average acceleration


  The rate at which velocity changes
• Average acceleration equation

  average acceleration = delta v / delta t
• m/s^2


  Units of acceleration
• Deceleration


  When an object's acceleration is opposite to the direction of its motion
• A racehorse coming out of the gate accelerates from rest to a velocity of 15.0 m/s due west in 1.80 s. What is its average acceleration?

  -8.33 m/s^2
• Instantaneous acceleration or a


  The acceleration at a specific instant in time
• An airplane lands on a runway traveling east. Describe its acceleration.

  If we take east to be positive, then the airplane has negative acceleration, as it is acceleration towards the west. It is also decelerating: its acceleration is opposite to the direction of its velocity
• A jogger runs down a straight stretch of road with an average velocity of 4.00 m/s for 2.00 min. What is his final position, taking his initial position to be zero?

  480 m
• Equation for solving displacement and final position from average velocity with acceleration is constant

  x = x_0 + average velocity X t, where average velocity = (v_0 +v) / 2
• Equation for final velocity


  v = v_0 + a X t
• An airplane lands with an initial velocity of 70.0 m/s and then decelerates at 1.50 m/s^2 for 40.0 s. What is the final velocity?

  10.0 m/s
• Equation for final position when velocity is not constant


  $x =$$x_0+$$v_0*$$t+$$1/2*$$a*$$t^2$
• Dragsters can achieve accelerations of 26.0 m/s^2. Suppose such a dragster accelerates from rest at this rate for 5.56 s. How far does it travel in this time?

  402 m