Velocity and Acceleration in Two Dimensions. Review of Average Speed A family drives from Saint John, New Brunswick, to Moncton. Assuming a straight highway,

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Presentation transcript:

Velocity and Acceleration in Two Dimensions

Review of Average Speed A family drives from Saint John, New Brunswick, to Moncton. Assuming a straight highway, this part of the drive has a displacement of km [E 32.1° N]. From Moncton, they drive to Amherst, Nova Scotia. The second displacement is 51.9 km [E 25.9° S]. The toal drive takes 2.5 h to complete. –Calculate the average velocity of the family’s vehicle. –Calculate the average speed of the family’s vehicle.

Subtracting Vectors in Two Dimensions Multiplication of a vector by a scalar changes the vector’s length If a scalar, k, is greater than 1 (k > 1), then the product of k and vector A is longer than A If 0 < k < 1, then the product of k and vector A is shorter than A If the scalar k is negative (k < 0), then the vector points in the opposite direction

Subtracting Vectors in Two Dimensions Vector subtraction is equivalent to adding a positive vector and a negative vector Ex: subtracting vector B by from vector A is equivalent to adding the vectors A and –B

Subtracting Vectors in Two Dimensions Example: a car is following a curved road. Even if the driver keeps the speed of the car constant, the direction of the car changes. This change equals the difference between the velocity at one point in time and the velocity at any earlier point in time. Therefore, the change in velocity is the subtraction of the final and initial velocities

Acceleration in Two Dimensions A car turns from a road into a parking lot and into an available parking space. The car’s initial velocity is 4.0 m/s [E 45.0° N]. The car’s velocity just before the driver decreases speed is 4.0 m/s [E 10.0° N]. The turn takes 3.0s. Calculate the average acceleration of the car during the turn.

Do the practice problems on page 34

Classwork/Homework Page 35 #’s: 2, 3, 6, 7, 9