Displacement - change of position in a particular direction

Speed - time rate of motion

Average speed - total distance divided by elapsed time

Instantaneous speed slope of the line tangent to the curve at a given point

Velocity - speed in a particular direction

Average velocity - total displacement divided by total elapsed time

vavg = (x – x0) / (t – t0) vavg = ∆x / ∆t

Example: Fluffy runs with an average velocity of 7. 05 m/s east Example: Fluffy runs with an average velocity of 7.05 m/s east. What distance does she cover in 57 s?

In a displacement vs. time graph, the slope is the velocity.

Instantaneous velocity - velocity of a moving body at a particular moment in time

Instantaneous velocity may not be the same as average velocity.

Acceleration - the time rate change of velocity

aavg = (v – v0)/(t – t0) aavg = ∆v / ∆t

Example: A school bus slows to a stop with an average acceleration of -2.0 m/s2. How long does it take the bus to slow from 18.0 m/s to 0.0 m/s?

Galileo Galilei was the first scientist to understand the concept of acceleration.

In a velocity vs. time graph, the slope is the acceleration.

Displacement depends on acceleration, initial velocity, and time.

∆x = 1/2 (v + v0)∆t

Example: A racing car moving at 50 m/s begins a uniform negative acceleration, using its parachute and brakes, and comes to rest 5.0 s later. How far does the car move while stopping?

The final velocity of an object starting from rest and accelerating at constant velocity is the product of the acceleration and the time elapsed.

aavg = (v – v0)/∆t v = v0 + a ∆t

v = v0 + a ∆t If the object starts from rest, v0 = 0, and v = a ∆t

∆x = v0∆t + 1/2 a∆t2

If the object starts at rest: ∆x = 1/2 a∆t2 (v0∆t = 0)

Example: A plane starting from rest undergoes a uniform acceleration of 5.6 m/s2 for 12 s. What is its speed at takeoff? How long must the runway be?

v2 = v02 + 2a∆x

If the object starts from rest: v2 = 2a∆x (v02 = 0)

Example: A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.40 m/s2. What is the velocity of the stroller after it has traveled 5.0 m?

Example: Starting from rest, a ball rolls down an incline at a constant acceleration of 3.00 m/s2. (a) What is the velocity of the ball after 5.0 s? (b) How far does the ball roll in 10.0 s?

Example: A car traveling at 60 m/s undergoes a constant deceleration of 8.0 m/s2. (a) How long does it take the car to come to a stop? (b) How far does the car move after the brakes are applied?

Example: An object starts from rest and moves with constant acceleration for a distance of 160 m in 6.0 s. What is the acceleration of the object?