Relative Speed

The relative speed of two objects is the vector sum of their speeds. The formula that calculates it also considers their masses and the displacement vector between them. Calculating relative speed is necessary for calculating the momentum of an object and its direction in a multi-body system. The formula that calculates the speed of an object divided by t (t is equal to the time elapsed since some initial frame), called the rate of change of speed, is based on Newton’s second law. This is the fundamental equation for calculating relative speed. Relative speed helps you understand how far something has travelled in a given amount of time.

Meaning of Relative Speed

The relative speed of two objects is their speed divided by the mass of one object. An object with a greater relative speed can exert more momentum on another object. It is very useful for calculating the final direction of one moving body if it collides with another stationary or moving body.

The relative speed formula requires an acceleration relation between the objects and an initial speed of each object (assuming zero initial displacements).

The acceleration relation between the two objects can come from any force relations or potential relations that exist between them, such as gravitational potential or Coulomb’s law.

Accuracy: This equation does not require acceleration relations between the objects. It is more accurate than equations that do require them. Even without an acceleration relation, this equation is still the most accurate formula for calculating the relative speed of two objects.

Term: The number of terms in the vector sum can be determined by using this formula and dividing it by time. The first term is the normalised total mass of both objects. The second is the acceleration of each object. The last term is the acceleration of one object divided by its mass. This means that if one object increases or decreases its speed while another object remains constant, relative speed will increase or decrease, respectively.

Acceleration: Acceleration is directly related to speed. When one object accelerates towards another object, the relative speed of both objects increases if we divide it by the mass of one object, this is why large objects have very low relative speeds.

Relation Between Speed, Distance, and Time

Distance and time are inversely related. If one object decreases its speed by dividing by a smaller number, the distance between them will increase. If the object increases its speed by dividing by a larger number, the distance between them will decrease.

The Explanation for the Relative Speed

When two objects are moving, there is a relative speed between them. This is because both of their speeds are changing all the time. The relative speed can be calculated by adding the speeds of one object to that of another. If one object remains constant while the other moves, there will be a speed difference between them; this will result in a final relative speed different from the sum of initial speeds.

Example of Relative Speed

We can understand the relative speed formula by understanding the relationship between speed, time, and distance.

Suppose that one object has a speed of 150 m/s while another object has a velocity of -50 m/s. If both objects move at the same speed of 150 m/s, their relative speeds are still 50 m/s, but their total mass differs. Their speeds are all different because their masses are different. If one object accelerates or decelerates, the relative speed between the two objects changes. Because this only applies to non-zero displacements of both objects, it is more accurate than previous equations for calculating relative speed.

Applications of Relative Speed

Relative speed has many applications in solving day-to-day problems.

• Calculate the final direction of a moving body if it collides with another moving or stationary body.
• Determining the total momentum of one moving object if it collides with another moving or stationary object.
• Determining the relative speed between two objects moving in different directions since their velocities differ.
• Calculate the mass of one object if it collides with another object at a certain speed and velocity.
• Determining the force of attraction between two objects if they are both moving together or apart at a given relative speed.
• Calculating the kinetic energy of one object if it collides with another at a certain speed and velocity.
• Calculating the energy of one object if it accelerates towards another at a certain speed and velocity.
• Calculate the final distance between two objects if they collide with each other and are not moving in the opposite direction after collision.
• Finding the direction of force relation between two objects moving in equal directions (such as F=ma).

Conclusion 

The relative speed of two objects is how fast one object is moving with respect to another. Relative speed can be positive, meaning the first object is going in the same direction as the second, or negative, meaning the first object is going in a different direction from the second.

The relative speed formula uses symbols that you might find on your calculator: “>” means ‘is greater than, “<” means ‘is less than, and “=” means ‘equals.’ If the notation uses the plus sign, meaning that the first object (the one doing the moving) is going in a direction to which it is pointing.