Motion in One Dimension Acceleration

What We Need To Know What is acceleration? How are the directions of velocity and acceleration related to the actual motion of an object? How are displacement, velocity, time, and acceleration related?

What We Know Δx v = t What is displacement? Straight line from where you start to where you end. Positive and negative numbers tell us what? Direction What is the difference between scalars and vectors? Both have magnitude, but only vectors have direction. How do you determine velocity? v = Δx t

Average Velocity xi x ti xf tf t Time Position xi x ti Rise over run… the slope of a position time graph gives velocity xf tf t

Changing Velocity If either an object’s velocity or direction are changing then the object’s velocity is changing.

Acceleration Acceleration (a) is the rate of change of velocity over time. How fast velocity is changing. Acceleration or… = change in velocity time interval _____________ _____ t vf - vi a = ___ t ∆v a =

Instantaneous Velocity Vi Vf Just like position, we can identify the object’s velocity at any instant by reading a clock At ti, the velocity is vi … At t , the velocity is v

Velocity vs. Time Graphs On a velocity vs. time graph, you can determine graphically an objects velocity at any given time (instantaneous velocity) Time Velocity

Discuss + is right, - is left Which direction is the object moving at A? At which point(s) is acceleration occurring? At which point(s) is there constant velocity? What is happening at D? 10 C Velocity B A Time D -10

Average Acceleration vf vi ti tf Time Velocity ti vi t2 v2 . tf vf We can use instantaneous velocity and time to help understand how an object’s velocity changes over time. Velocity vf vi The slope of a velocity vs. time graph gives acceleration ti tf Time

Acceleration and Displacement The slope of the velocity versus time graph represents acceleration Velocity How do you find area under the graph? (It’s a triangle) The area is a function of velocity multiplied by time V t v How do we figure out area? ½ base times width, so ½ v times t. Wait hold on to that. Have v = Δx/t on the board so I can show Δx = vt The area under the velocity versus time graph represents displacement t Time

Displacement and Acceleration Constant Acceleration Area = ½ (vf – vi)t + vi . t Vi t Vf We know the area represents displacement, so…. Δx = ½ (vf - vi)t + vit or, Dx = ½ (vf + vi)t

Constant Acceleration Equations: Symbol Variable Units Δx displacement m v velocity m/s t time s a acceleration m/s2 ∆x = (vf + vi)t 1 _ 2 ∆x = vit + at² 1 _ 2 vf² = vi² + 2a∆x

Acceleration and Direction Displacement, Velocity, and Acceleration must have a magnitude and direction In 1-D, direction is positive or negative Will displacement, velocity, and acceleration always go in the same direction (same sign)? -1 1 2 3 4 5 6 X (meters) + -

Velocity vs Acceleration Object’s Motion + Speeding Up in the positive direction - Slowing Down in the positive direction Speeding Up in the negative direction Slowing Down in the negative direction -/+ Speeding Up from at rest At Rest

Graphs of Constant Acceleration distance velocity acceleration time

Example An aircraft has liftoff speed of 120 km/h. What is the minimum acceleration required if the aircraft needs to be airborne after 240m? If a car initially traveling at 5 m/s accelerates at a rate of 3.0 m/s2: What was the car’s final speed after 8 seconds? How far did the car travel?

What We Now Know What is acceleration? How are the directions of velocity and acceleration related to the actual motion of an object? How are displacement, velocity, time, and acceleration related?