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**Physics Lab 2 Graphical Analysis of Motion**

Eleanor Roosevelt High School Chin-Sung Lin

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Speed & Velocity

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**Speed v = d / t A speed (v) is a scalar quantity**

Distance (d) covered per unit of time (t). Speed is a measure of how fast something is moving. It is the rate at which distance is covered v = d / t Unit: meters per second (m/s), miles per hour (mi/h), kilometers per hour (km/h)

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**Velocity A velocity (v) is a vector quantity**

Velocity is the measurement of the rate and direction of change in the displacement (d) of an object v = d / t The speed is the magnitude of velocity Unit: meters per second (m/s), miles per hour (mi/h), kilometers per hour (km/h)

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**Speed & Velocity Speed has only magnitude**

Velocity has magnitude and direction

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**Average Speed Average speed (v): v = d / t**

d = total distance covered (m) t = time interval (s) d slope = v t

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Instantaneous Speed The speed (v) at any instance of an object is called the instantaneous speed It is equal to the slope of the tangent line at that moment d slope = v t

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**Average Velocity Average velocity (v): v = d / t**

d = total displacement (m) t = time interval (s) d slope = v t

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**Instantaneous Velocity**

The velocity (v) at any instance of an object is called the instantaneous velocity It is equal to the slope of the tangent line at that moment d slope = v t

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Acceleration

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**Acceleration An acceleration (a) is a vector quantity**

acceleration is the rate of change of velocity with time a = Δv / t a = acceleration (m/s2) v = change of velocity (m/s) t = time interval (s)

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**Acceleration a = Δv / t An acceleration (a) is also a scalar quantity**

When linear (straight-line) motion is considered, it is common to use speed and velocity interchangeably and the acceleration may be expressed as the rate at which speed changes a = Δv / t a = acceleration (m/s2) v = change of speed (m/s) t = time interval (s)

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**Acceleration Acceleration: the slope of the speed-time (v-t) graph v**

slope = ax (acceleration) t

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**Constant Acceleration**

The acceleration at any instance of an object is constant In high school physics, we only deal with constant acceleration v a slope = ax slope = 0 ax t t

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**Distance-Time Formula**

Given initial speed (vi) and time (t), and acceleration (a), the distance-time formula If the initial speed (vi) is 0, then d = vit + ½ at2 d = ½ at2

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**Distance-Time Formula**

The distance-time formula is a quadratic function!!! Compare to the standard form of quadratic function: d = ½ at2 d-t t d y = ax2

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**Distance, Speed & Acceleration**

d-t v-t a-t d slope = increasing at constant rate v a slope = ax slope = 0 ax t t t

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The End

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