Acceleration in One and Two Dimensions

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Presentation transcript:

Acceleration in One and Two Dimensions Acceleration: The rate of change in velocity Can be found by: Determining the slope of a straight-line velocity-time graph (uniform acceleration) Determining the slope of the tangent to a curved velocity-time graph (instantaneous acceleration) Determining the slope of a straight-line segment joining two points on a curved velocity-time graph (average acceleration) Using the following equation of motion if initial velocity, final velocity and time are known:

is a vector quantity, so in 2-dimensions a vector diagram (and trigonometry) is required for addition/subtraction Example: Selma is driving her MicrobusTM directly South at 22 m/s when she makes a turn to a new heading of [E 15° S] with a new speed of 16 m/s. If the turn takes 7.2 s, what is her average acceleration?

Δv = ? - v1 = 22 m/s 15° v2 = 16 m/s

Δv = ? 17.86 m/s θ 15.45 m/s

Free Fall any object that is only under the influence of gravity falls with constant acceleration (9.8 m/s2 on Earth) includes objects that are dropped, kicked, thrown or tossed, as long as they are in mid-air. Galileo first identified this constant acceleration. We can use the five equations of motion to solve problems involving free-falling objects:

Example: Iggy throws a baseball straight up from his 5.5 m high balcony with a speed of 22 m/s. a) What is the speed of the ball when it strikes the ground? b) How long after he throws it does it reach the ground? c) What is the ball's maximum height?

so the maximum height of the ball is (24.7 + 5.5) = 30.2 m [above the ground].