Physics Chapter 3 and 5

Velocity, Acceleration, and Falling Bodies

Reference Point – the point that all objects are measured from

• What is similar about these two clips?• What is different about these two clips?• They are similar because they both traveled the same

distance (10 yards)• The are different because one traveled forward and the

other traveled backwards.

Scalars vs. Vectors

• The distance is the separation between objects. It does not have a direction and is called a scalar

• The position or displacement is the separation between the object and the reference point. It does have a direction and is called a vector

Displacement

• Displacement – change in position;

• What is the displacement of the runner in the clip?

• 0 yards• What is the distance

traveled?• 20 yards

Speed and Velocity

• Speed is simply saying that Ed here is going 80 mph.

• Speed is a scalar.• Velocity is saying that

Ed is going 80 mph in a easterly direction.

• Velocity is a vector.

Velocity

• Average Velocity – the total displacement over the time interval

• v = df – di / tf – ti

• Constant velocity – the average velocity is the same for all time intervals – Zero acceleration

Question

• Is a merry go round experiencing constant speed or constant velocity?

• The answer is …• Constant speed because its direction is

constantly changing.

Position-Time Graphs

• Instantaneous position – the location of an object at a single instant

• The slope on a position-time graph gives you constant velocity

Curves on a P-T GraphConstant positive velocity(going forward)

Constant negative velocity(going backward)

Zero Velocity (not moving)

AcceleratingPosition

Time

Position-Time Graph

15

10

5

Met

ers

(m)

2 4 6 8 10 12 14

Time (s)

Find the:

• Displacement after 4 seconds

• Displacement after 14 seconds

• Distance traveled after 14 seconds

• Velocity from 0-4 sec• Velocity from 4-10 sec• Velocity from 10-14 sec• Acceleration from 0-4 sec

• 10 m

• 0 m

• 20 m• 2.5 m/s• 0 m/s• -2.5 m/s• 0 m/s2

Velocity-Time Graphs

• Instantaneous velocity – velocity of an object at a single instant

• Ex: Your speedometer

• V-T graphs: the slope of these graphs gives you acceleration

• Also, the area under the curve of a velocity-time graph gives you the displacement

Acceleration

• Acceleration is the change in velocity.

• A = Vf – Vi / t

Curves on a V-T GraphConstant positive acceleration(speeding up in positive direction)

Constant negative acceleration(slowing down in positive direction

Zero acceleration(constant positive velocity)

Constant positive acceleration(Slowing down in the negative direction)

Constant negative acceleration(speeding up in the negative direction)

Zero acceleration(constant negative velocity)

Velocity

Time

15

10

5

Vel

ocity

(m

/s)

1 2 3 4 5 6 7

Time (s)

8 9

Velocity-Time Graph

Find the:

• Velocity after 2 sec• Velocity after 9 sec• Acceleration from 0-2 s• Acceleration from 2-4s• Acceleration from 4-6 s• Acceleration form 6-9s• Displacement from 0-2 s• Displacement from 0-9 s

• 10 m/s• 0 m/s• 5 m/s2

• 0 m/s2

• 2.5 m/s2

• -5 m/s2

• 10 m• 77.5 m

Relative Velocity

• Always remember that motion is relative.

• The earth is usually our reference point to determine our speed.

• We are all traveling the same speed relative to the sun.

Relative Velocity

45 MPH

60 MPH

•What is the velocity of the blue car relative to the green car?•15 mph•What is the velocity of the green car relative to the blue car?•-15 mph

Relative Velocity

55 MPH

40 MPH

•What is the velocity of the blue car relative to the red car as they head towards one another?•95 mph•What is the velocity of the blue car relative to the red car as they head away from one another?•-95 mph

Motion Equations

• v= v0+at

• d= 0.5(v+v0)t

• d = V0t + 0.5at2

• v2 = v02 + 2ad

• V = final velocity

• V0 = initial velocity

• d= displacement• a= acceleration• t = time

Freefall

• a= g = -9.8m/s2

• If something is dropped v0 = 0

• At its highest point, an object’s velocity is 0

• If an object is falling its displacement is negative.