Relative Speed

The idea of relative speed is used to compare the speeds of two or more bodies travelling at different rates. To simplify things, one body can be made stationary (i.e. Speed = 0), and the speed of the other body in relation to the stationary body can be calculated as the total of the speeds if the bodies are travelling in opposing directions, or as the difference if they are travelling in the same direction. The speed of a moving body in relation to the speed of a stationary body is referred to as relative speed. 

Relative speed meaning

In other terms, the velocity of one item as measured from another object is referred to as its Relative Speed. The relative speed can be divided into two categories, as indicated below.

Objects  moving in the same Direction

Let’s imagine two objects are moving in the same direction with velocities equal to a and b with respect to the ground. Let’s say you and your friend are both taking the train, or you’re on the train and she’s in the car, but you’re both going to the same place. Let your velocity be a and your friend’s velocity be b. Then, as observed by you, your friend’s Relative Speed is equal to:

a – b

This is referred to as the Relative Speed of a in relation to b.

Objects  moving in the opposite Direction

Let’s imagine you’re travelling from Bombay to Pune, and your friend is travelling in the opposite direction from Pune to Bombay. The Relative Speed is thus defined as (a + b) or the total of the two velocities.

Example 1: A bus is travelling at a constant 55 mph on a straight highway. A passenger on the bus discharges a dart pistol with a muzzle velocity of 45 miles per hour straight rearward (toward the back of the bus). Calculate the dart’s velocity as it leaves the gun in relation to the road.

Answer: By defining VBR as the bus’s velocity relative to the road, VDB as the dart’s velocity related to the bus, and VDR as the dart’s velocity relative to the road, and the forward direction as the positive direction, we get:

VDR  = VBR – VDB , or, to put it another way, VBR= 55 mph, VDB = 45 mph. As a result, we can write VDR  = 10 mph in the direction of travel for the bus.

Formula of relative speed

The formula below explains how to use the traditional approach to calculate the constant velocity of an object travelling in a straight line.                                

r = d / t

r → Rate or speed 

d→ Distance travelled 

t → Amount of time it takes to execute an activity

The above equation calculates an object’s average speed over a period of time. The item may move faster or slower at different times throughout the time span. The average speed is calculated by dividing the total distance travelled by the total time taken.If two bodies are moving in the same direction at different speeds, the difference between their speeds can be used to calculate their relative speed. It can be phrased as follows:

When bodies travel in the same direction, relative speed is determined by:

                                       V1 – V2

If two bodies are moving in opposite directions at different speeds, the total of their speeds can be used to calculate their relative speed. It can be phrased as follows:

When two bodies move in the same direction, relative speed is determined.

                               V1+V2

Where,

V1 is the first body’s speed.

V2 is the second body’s speed.

Relative speed of approach and separation

The relative speed of separation of colliding objects is the same as the relative speed of approach of the two in an elastic collision.

If the two object’s approach speeds are v1,v2 and their separation speeds are V1‘,V2‘, respectively, then:

                     V1+V2=V1’+V2’

Because there is no external force acting on the system, the linear momentum of colliding systems is always conserved, in both elastic and inelastic cases.

Conclusion

Speed is defined as the rate at which an object travels over a given distance. A fast-moving object moves quickly and covers a considerable distance in a short period of time, whereas a slow-moving object moves slowly and covers a little distance in the same amount of time. The magnitude of an object’s speed in everyday use and kinematics is the magnitude of the rate of change of its position with time or the magnitude of change of its position per unit of time. The speed of light is impossible to reach since it would require an infinite amount of energy. In relativistic physics, the concept of rapidity has supplanted the classical concept of speed.