Question

A car moves from X to Y with a uniform speed v_u and returns to Y with a uniform speed v_d. The average speed for this round trip is:

$fraction numerator 2 straight v subscript straight d straight v subscript straight u over denominator straight v subscript straight d plus straight v subscript straight u end fraction$
$square root of straight v subscript straight u straight v subscript straight d end root$
$fraction numerator straight v subscript straight d straight v subscript straight d over denominator straight v subscript straight d plus straight v subscript straight u end fraction$
$fraction numerator straight v subscript straight u space plus straight v subscript straight d over denominator 2 end fraction$

Solution

fraction numerator 2 straight v subscript straight d straight v subscript straight u over denominator straight v subscript straight d plus straight v subscript straight u end fraction

The average speed of a body in a given time interval is defined as the ratio of distance travelled to the time taken.
$Average space speed space equals space fraction numerator Distance space travelled over denominator Time space taken end fraction$
Let t₁ and t₂ be times taken by the car to go from X and Y and then Y to X respectively.
Then,
$straight t subscript 1 space plus straight t subscript 2 space equals space XY over straight v subscript straight u space plus XY over straight v subscript straight d space equals space XY space open parentheses fraction numerator straight v subscript straight u space plus straight v subscript straight d over denominator straight v subscript straight u straight v subscript straight d end fraction close parentheses Total space distance space travelled equals space XY space plus space XY space equals space 2 XY Therefore comma space average space speed space of space the space car space for space this space round space trip space is straight v subscript av space equals space fraction numerator 2 XY over denominator XY open parentheses begin display style fraction numerator straight v subscript straight u plus straight v subscript straight d over denominator straight v subscript straight u straight v subscript straight d end fraction end style close parentheses end fraction or straight v subscript av space equals space fraction numerator 2 straight v subscript straight u straight v subscript straight d over denominator straight v subscript straight u plus straight v subscript straight d end fraction$

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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

What is a scalar quantity?

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

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