A body travelling along a straight line traversed one-third of the total distance with a velocity 4 m/s. The remaining part of the distance was covered with a velocity 6 m/s for the other half of time. What is the mean velocity averaged over the whole time of motion?

Solution

Let s be the total distance travelled by body.
If t₁ is the time taken to cover first one-third distance, then

$straight t subscript 1 space equals space fraction numerator straight s divided by 3 over denominator 4 end fraction space equals space straight s over 12 space$
Let t₂ be the time for each of the remaining two journeys.
Then,

$fraction numerator 2 straight s over denominator 3 end fraction space equals space 2 t subscript 2 space plus space 6 t subscript 2 space space space space space space space space space equals space 8 t subscript 2$

$straight t subscript 2 space equals space fraction numerator 2 straight s over denominator 3 space straight x 8 end fraction space equals space straight s over 12 space$
Therefore,
Average velocity = $fraction numerator Total space displacement over denominator total space time end fraction$
= $fraction numerator straight s over denominator straight t subscript 1 space plus space 2 straight t subscript 2 end fraction space equals space fraction numerator s over denominator left parenthesis s divided by 12 right parenthesis space plus space 2 left parenthesis s divided by 12 right parenthesis end fraction space equals space 4 space m divided by s$

Some More Questions From Motion in A Plane Chapter

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.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

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Motion In A Plane

A body travelling along a straight line traversed one-third of the total distance with a velocity 4 m/s. The remaining part of the distance was covered with a velocity 6 m/s for the other half of time. What is the mean velocity averaged over the whole time of motion?

Some More Questions From Motion in A Plane Chapter

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.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

A body travelling along a straight line traversed one-third of the total distance with a velocity 4 m/s. The remaining part of the distance was covered with a velocity 6 m/s for the other half of time. What is the mean velocity averaged over the whole time of motion?

Some More Questions From Motion in A Plane Chapter

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.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.