## Velocity-Time Graphs

A velocity-time (v-t) graph shows an object's velocity as a function of time.

A horizontal line = constant velocity

If an object is NOT moving = velocity is 0

If the graph has a

If the graph has a

How can you tell when an object is speeding up or slowing down?

When the v-t line has a POSITIVE SLOPE, and the velocity is also positive (5m/s), the object is speeding up. When the v-t line has a POSITIVE SLOPE and the velocity is negative (-5m/s), the object is slowing down.

When the v-t line has a NEGATIVE SLOPE, and the velocity is positive (5m/s), the object is slowing down. When the v-t line has a NEGATIVE SLOPE and the velocity is also negative (-5m/s), the object is speeding up.

The slope of the line on a position-time graph represents velocity (change in position/change in time).

The slope of the line on a velocity-time graph represents acceleration (change in velocity/change in time).

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A horizontal line = constant velocity

If an object is NOT moving = velocity is 0

If the graph has a

__positive slope__, then the object is undergoing acceleration in the positive direction (usually above the origin)If the graph has a

__negative slope__, then the object is undergoing acceleration in the negative direction (usually below the origin)*You have to make sure that your v-t graph has a CLEAR negative component.*__Acceleration:__If the v-t graph has a positive slope, the object is undergoing acceleration in the POSITIVE direction (not necessarily speeding up). If the v-t graph has a negative slope, the object is undergoing acceleration in the NEGATIVE direction (not necessarily speeding up).How can you tell when an object is speeding up or slowing down?

When the v-t line has a POSITIVE SLOPE, and the velocity is also positive (5m/s), the object is speeding up. When the v-t line has a POSITIVE SLOPE and the velocity is negative (-5m/s), the object is slowing down.

When the v-t line has a NEGATIVE SLOPE, and the velocity is positive (5m/s), the object is slowing down. When the v-t line has a NEGATIVE SLOPE and the velocity is also negative (-5m/s), the object is speeding up.

**UNDERSTAND:**The slope of the line on a position-time graph represents velocity (change in position/change in time).

The slope of the line on a velocity-time graph represents acceleration (change in velocity/change in time).

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## Acceleration

Acceleration is defined as the rate which an object changes its velocity. It has nothing to do with going fast. A person can be moving very fast yet not be accelerating. If an object is NOT changing its velocity, then it is NOT accelerating.

Acceleration and velocity are different quantities. A large acceleration represents a rapid CHANGE in velocity, but tells you nothing about the magnitude or direction of the velocity.

An accelerating object can change its velocity by the same amount each second. This is referred to as constant acceleration. An object with constant acceleration should not be confused with an object with constant velocity. I

Example:

Object B Object K

Time (s) Velocity (m/s) Time (s) Velocity (m/s)

0 0 0 0

1 4 1 1

2 8 2 4

3 12 3 5

4 16 4 7

Object B is undergoing constant acceleration. Object K is undergoing non-constant acceleration.

Since acceleration is a velocity change over time, the unit is a velocity unit divided by a time unit (seconds). Values are typically written as m/s/s m/s2, mi/hr/s, or km/hr/s.

This is when gravity pulls down on falling objects. Standard unit is (g).

An object in free fall is an object acted upon by gravity alone. Said object will experience a pure acceleration due to gravity (and nothing else). A free falling object has an acceleration of -9.8m/s2. (negative indicates direction; downward)

How this affects the quantities of velocity, distance and time are represented by the following motion equations:

d = 1/2at2 (a squared)

a = 2d/t2 (t squared)

t = √2d/a (square root of 2d/a)

a = vf/t (for an object starting from rest; vf is final velocity [initial is always 0]).

a = acceleration, t = time, d = displacement (change in position)

When solving these problems, do the following: (1) Identify your known quantities, (2) Determine what's being asked, and (3) Select the best equation to solve the problem.

Acceleration and velocity are different quantities. A large acceleration represents a rapid CHANGE in velocity, but tells you nothing about the magnitude or direction of the velocity.

An accelerating object can change its velocity by the same amount each second. This is referred to as constant acceleration. An object with constant acceleration should not be confused with an object with constant velocity. I

__f an object is changing its velocity (whether constantly or varying), then it is accelerating. And an object with constant velocity is NOT accelerating.__Example:

Object B Object K

Time (s) Velocity (m/s) Time (s) Velocity (m/s)

0 0 0 0

1 4 1 1

2 8 2 4

3 12 3 5

4 16 4 7

Object B is undergoing constant acceleration. Object K is undergoing non-constant acceleration.

Since acceleration is a velocity change over time, the unit is a velocity unit divided by a time unit (seconds). Values are typically written as m/s/s m/s2, mi/hr/s, or km/hr/s.

__Acceleration Due to Gravity__This is when gravity pulls down on falling objects. Standard unit is (g).

An object in free fall is an object acted upon by gravity alone. Said object will experience a pure acceleration due to gravity (and nothing else). A free falling object has an acceleration of -9.8m/s2. (negative indicates direction; downward)

How this affects the quantities of velocity, distance and time are represented by the following motion equations:

d = 1/2at2 (a squared)

a = 2d/t2 (t squared)

t = √2d/a (square root of 2d/a)

a = vf/t (for an object starting from rest; vf is final velocity [initial is always 0]).

a = acceleration, t = time, d = displacement (change in position)

When solving these problems, do the following: (1) Identify your known quantities, (2) Determine what's being asked, and (3) Select the best equation to solve the problem.