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.
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.