Advanced Physics

Rotational Motion and Astrophysics

# Kinematic Relationships

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Kinematic Relationships

**Kinematic Relationships**

**Constant Speed**

- Fundamental definition of
**speed**is distance divided by time. - For an object travelling at a constant speed -
**distance = speed x time**. - Use
**scalar**terms, speed is a scalar quantity, it has magnitude but no direction.

**Constant Acceleration**

- Acceleration is defined as the rate of
**change of velocity**per unit time. - For an object moving with constant acceleration, it follows three kinematic equations:
**final velocity = initial velocity + acceleration x time**.**distance= initial velocity x time + 0.5 x acceleration x time squared**.**final velocity squared = initial velocity squared + 2 x acceleration x distance**.

**Variable Acceleration**

- Acceleration is variable when it is changing over time.
- In this case, apply
**calculus**to find displacement or velocity. - The derivative of displacement yields
**velocity**, and its double derivative yields**acceleration**.

**Circular Motion**

- Circular motion is a special case where the object moves along a circular path.
- It has a constant speed but changing direction, hence it has acceleration known as
**centripetal acceleration**. - Key kinematic equations for circular motion:
- Centripetal acceleration =
**velocity squared / radius**. - Velocity for an object in circular motion =
**2 x Pi x radius / Time of one complete revolution**.

- Centripetal acceleration =

**Projectiles**

- Projectiles are objects launched into the air and subject to gravity.
- The motion of a projectile has both
**horizontal and vertical components**. - Horizontal motion has constant velocity while vertical motion has constant acceleration due to gravity.
- The maximum height, range and time of flight can be calculated using the principles of kinematics.

**Motion in a Straight Line**

- This refers to linear motion where an object travels along a straight path or line.
**Displacement**is the total distance travelled in a specific direction which makes it a vector quantity.- Linear motion example relates to Newton’s First law of Motion where an object continues to stay at rest or in motion until acted upon by an external force.