Motion in One and Two Dimensions

1
Motion in One and Two Dimensions

• Magnitude- the amount or size of something.
  Usually a numeric value. Positive values for
  all but temperature.
• Scalar- an object that only has magnitude, but
  direction does not apply.
• Examples time, distance, mass, temperature,
  speed
• Vector- a quantity that has both magnitude and
  direction, and can be positive or negative.
• Examples- displacement, velocity, acceleration.

2

• Distance the measure of how far objects
• d, x, y or locations are spaced from
  each other Unit meters Scalar
• Displacement the measure of change in distance
• (x-x1), Dx from a starting point. Unit meters
• Ex 1 lap around the track is a distance
• of 400m, but a displacement of 0.
• Vector Can be negative!

3

• Vectors can be added and subtracted.
• If two vectors point in the same direction, they
  will add together to form a larger vector.
  (Largest sum)
• If two vectors point in opposite directions,
  they subtract, with the bigger vector indicating
  the direction of the result. (Smallest sum)
• EX Vectors 6m and 5m. Same direction, sum is
  11m. Opposite directions, 1m.

4

• Resultant the final vector that represents
• the combination of a series of
• vectors.
• Ex If vectors are at right angles, Use
  Pythagorean Thm to find Resultant.
• Components the x and y vectors that add
• together to form the resultant.
• EX Vector length 10, at 300, find the
• x and y components. (draw a right triangle)

5

• Trig functions- sine, cosine, tangent are useful
  to resolve the vectors into components, and to
  solve for missing angle. (Use only with right
  triangles)
• SOH- CAH- TOA
• Sine the ratio of the side opposite the angle,
  and the hypotenuse.
• (Sine q Opposite/Hypotenuse)
• Cosine the ratio of the side adjacent the
• angle, and the hypotenuse.
• (Cosine q Adjacent/ Hypotenuse)

6

• Tangent the ratio of the side opposite the
• angle to the side adjacent to the
• angle. (Useful in finding missing
• angle measures)
• (Tangent q Opposite / Adjacent)
• Example 1 Find the x and y components of a
  velocity that is 25 m/s at 400 to the horizontal)
• Example 2 A hill is 80m long, and 15m high.
  What is the angle of the slope?

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• Speed the measure of how fast something is
• v, traveling. Average speed is the speed v
  x/t that we calculate from start to finish.
  Direction does not matter, only how fast.
  Scalar Units m/s
• Velocity the change in displacement over time.
• v, velocity is a vector, the direction is
• V (x-x1)/t important. You can have a negative
  
• velocity. Units m/s Vector
• Instantaneous the velocity at a specific instant
  in time.
• Velocity vf v1 at
• vf

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• Acceleration the rate at which the velocity
  changes
• a, m/s2 over time. A negative acceleration can
• indicate an object slowing down, this is
• often called deceleration. If the velocity
• a (v-v1)/t does not change, the acceleration is
  0.
• Kinematic equations
• 1st equation v v1 at
• 2nd equation x x1 v1t ½ at2
• 3rd equation v2 v02 2 a(x-x0)