Motion

Chapter 11

• Motion is an object’s change in position relative to a reference point.

• Displacement is the change in the position of an object.– Distance measures the path taken.– Displacement is the change of an object’s

position. Displacement must always indicate direction.

Distance vs. Displacement

• Speed - distance traveled divided by the time interval during which the motion occurred. Speed describes how fast an object moves. S = d / t– Speed measurements involve distance and

time.– The SI units for speed are meters per second

(m/s).• constant speed -when an object covers

equal distances in equal amounts of time, it is moving at a

• Average speed - calculated as distance divided by time.

• Instantaneous speed - the speed at a given point in time.

• Velocity is the speed of an object in a particular direction.– Velocity describes both the speed and the direction.

• Resultant velocity - combined velocities

speed = distance

time v = dt

Velocity Metal stakes are sometimes placed in glaciers to help measure a glacier’s movement. For several days in 1936, Alaska’s Black Rapids glacier surged as swiftly as 89 meters per day down the valley. Find the glacier’s velocity in m/s. Remember to include direction.

1. List the given and the unknown values.

Given: time, t = 1 daydisplacement, d = 89 m down

the valleyUnknown: velocity, v = ? (m/s and direction)

2. Perform any necessary conversions.

To find the velocity in meters per second, the value for time must be in seconds.

t = 1 day = 24 h 60 min

1 h 60 s1 min

t = 86 400 s = 8.64 104 s

speed = displacement

time = dt

3. Write the equation for speed.

v = dt =

89 m8.64 104 s

(For velocity, include direction.)

v = 1.0 10–3 m/s down the valley

4. Insert the known values into the equation, and solve.

• Acceleration is the rate at which velocity changes over time. – An object accelerates if its speed, direction, or

both change.– Acceleration can be a change in speed.– Acceleration can be a change in direction.

• Uniform circular motion is constant acceleration

• Acceleration is the rate at which velocity changes.Acceleration Equation (for straight-line motion)

• acceleration is measured in meters per second per second (m/s/s) or m/s2

acceleration = final velocity – initial velocity

time a = ∆vt

Acceleration A flowerpot falls off a second-story windowsill. The flowerpot starts from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. Find the average acceleration of the flowerpot.

1. List the given and the unknown values.Given: time, t = 1.5 s

initial velocity, vi = 0 m/sfinal velocity, vf = 14.7 m/s down

Unknown: acceleration, a = ? (m/s2 and direction)

3. Insert the known values into the equation, and solve.

a = vf – vi

t = 14.7 m/s – 0 m/s

1.5 s

a = 14.7 m/s

1.5 s = 9.8 m/s2 down

acceleration = final velocity – initial velocity

time = vf – vi

t

2. Write the equation for acceleration.

Acceleration can be determined from a velocity-time graph.

• Force - an action exerted on a body in order to change the body’s state of rest or motion. Force has magnitude and direction.• The net force is the combination of all forces

acting on an object.

• balanced forces - objects either do not move or move at constant velocity.

• unbalanced force - must be present to cause any change in an object’s state of motion or rest.

• Friction is a force that opposes motion between two surfaces that are in contact.– Friction opposes the applied force.

• Types of friction:

• Static

• Kinetic– Sliding– Rolling – fluid

• Static friction resists the initiation of sliding motion between two surfaces that are in contact and at rest.

• Kinetic friction opposes the movement of two surfaces that are in contact and are sliding over each other.– Static friction is greater than kinetic friction.

Frictional Forces & Acceleration

1. A bicyclist traveling at 10 m/s applies her brakes, reducing her velocity to 5 m/s. If it takes 2 seconds to slow the bike, what is the acceleration during that period?

A. –5 m/s2

B. –2.5 m/s2

C. 0 m/s2

D. 2.5 m/s2

What happens to a moving object when the forces acting on it are exactly balanced?A. The object gradually slows and stops moving dueto friction.B. The object moves at a constant speed, neither speeding up nor slowing down. C. The object accelerates because there is no friction to oppose the forces acting on it.D. The object accelerates because the force of gravity is stronger than friction.

3. For which of the following is the velocity constant?

A. a baseball traveling away from a bat after a hit

B. a bicyclist on an oval track moving at a constant speed of 15 km/h

C. a helicopter hovering motionless above a fixed point on the ground

D. a canoe being carried down a winding river by a steady current

4. When describing the motion of an object, why do you need a reference point?

5. A jet airplane must use a substantial amount of fuel to keep flying at a constant velocity. What two forces would change the velocity of the plane if the engines were shut off?