Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Relative velocity is the velocity of an object as observed from a frame of reference where another object is at rest.
For motion in a straight line, the relative velocity of object with respect to object is given by the vector difference of their velocities.
If two objects are moving in the same direction, the magnitude of their relative velocity is the difference of their speeds: .
If two objects are moving in opposite directions, the magnitude of their relative velocity is the sum of their speeds: .
The relative displacement between two objects at any time can be expressed as , where is the initial separation.
📐Formulae
💡Examples
Problem 1:
Two trains and are moving on parallel tracks with velocities and respectively in the same direction. Calculate the relative velocity of with respect to .
Solution:
.\ .\ .
Explanation:
Since both trains are moving in the same direction, we subtract the velocity of the observer (Train ) from the velocity of the object (Train ).
Problem 2:
Two cars and are apart. Car moves at and Car moves at towards each other. Find the time when they will meet.
Solution:
Velocity of () = .\ Velocity of () = (opposite direction).\ Relative velocity .\ Distance .\ Time .
Explanation:
When objects move towards each other, their relative speed increases (sum of magnitudes). The time of meeting is the initial separation divided by this relative speed.