Distance and Displacement PDF

Motion Distance and Displacement  Scalar vs. Vector A measurement A measurement that includes that includes both magnitude only magnitude and Examples: direction distance (50m) Examples: position (50 m [W]) speed (...

Motion Distance and Displacement  Scalar vs. Vector A measurement A measurement that includes that includes both magnitude only magnitude and Examples: direction distance (50m) Examples: position (50 m [W]) speed (10 km/h) velocity (10 km/h time (16 min) [N]) Acceleration (54m/s2[S])  Sign Conventions By convention: N=+ E=+ W=- S=- Up = + Down = - Right = + Left = -  Scalar vs. Vector Symbols for vectors are written with arrows above them while symbols for scalars are not. Ex. Speed = v (scalar) velocity = v (vector)  Distance (Δd) Scalar quantity Describes the length between 2 points Does NOT include direction Units: meters (m) Symbol = Δd The delta (Δ) represents a change in the location of the object.  Calculating Distance To calculate the distance between 2 points: Formula: d = df - di To calculate the total distance travelled: Formula: dT = d1+ d2 +...  Displacement (Δd) Vector quantity The length between 2 points as well as the direction. Units: meters (m) + [direction] Symbol = Δd The delta (Δ) represents the change in position.  Calculating Displacement To calculate the displacement between 2 points: Formula: d = df - di To calculate the total displacement: Formula: dT = d1+ d2 + … Distance Versus Displacement  Example 1 Find the displacement from position A to position B if dA = + 3.5cm and dB = +5.7cm. HINT: the word “from” suggests that you should subtract the 2 values because you are looking for the distance between the points.  Example 2 Find the displacement from position X to position Y if dx = 6.9m [E] and dy=8.2m[W]  Example 3 John walks 0.64km north and then walks 1.76km south. What was John’s total displacement? What was his total distance? HINT: the word “total” suggest that you should be adding the values together.