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A car moves from A to B with a speed of $30kmph$ and from B to A with a speed of $20kmph$. What is the average speed of the car?
$\left( A \right)25kmph$
$\left( B \right)24kmph$
$\left( C \right)50kmph$
$\left( D \right)10kmph$

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Last updated date: 20th Jun 2024
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Answer
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Hint: Here, the rate of change of displacement is called velocity. Average speed of a body undergoing linear motion is the ratio of total distance to total time. It is a scalar quantity. Here the speed to move from A to B and time to move from B to A is given. Using the given data, find the average speed of a car.

Complete step by step answer:
To describe the apposition of a body, its velocity or acceleration relative to frame of reference we use the kinematic equation. Velocity is the rate of change of displacement.
If the motion starts from rest and the frame of reference should be the same, the initial velocity will be zero. If the motion starts from rest and the frame of reference should be the same. It is a scalar quantity.
The body will move in uniform motion in a straight line, when the body is moving with uniform velocity.
Distance to unit time is called speed. Equation integration results in the distance equation.
Let us consider the distance travelled by the car from A to B to be $x$
The time taken by the car from A to B to be $ = \dfrac{x}{{30}}hour$
The time taken by the car from B to A to be $ = \dfrac{x}{{20}}hour$
Then we can calculate the average speed of the car is given by = $\dfrac{{Total{\text{ }}distance}}{{Total{\text{ time}}}}$
$\Rightarrow s = \dfrac{{x + x}}{{\dfrac{x}{{30}} + \dfrac{x}{{20}}}}$
On further simplification we get
Here $\left( {\left( {\dfrac{x}{{30}} + \dfrac{x}{{20}}} \right) = \left( {\dfrac{{2x + 3x}}{{60}}} \right) = \dfrac{x}{{12}}} \right)$
$\Rightarrow s = 2x \times \dfrac{{12}}{x}$
On multiply the term and we get
$\Rightarrow s = 24km/h$

Hence option B is the correct option.

Note: The motion starts from rest and the frame of reference should be the same. Then the initial velocity is zero. The velocity equation integration results in the acceleration equation. Displacement may or may not be equal to the path length travelled of an object. Distance to unit time is called speed.