After the engine of a moving motorboat is cut off, the motorboat retards with retardation directly proportional to v. What is the magnitude of velocity at any instant after the engine is cut off, if the velocity at the time of cut off is v₀?

Solution

Given,
Retardation of the boat, $tau space proportional to space nu$
Therefore,

r = kv; k is the proportionality constant.
$i. e. comma space straight a space equals space minus kv$
Now, we know that acceleration is given by rate of change of velocity.
$Rate space of space change space of space velocity space is space known space as space acceleration. space rightwards double arrow space dv over straight v space equals space minus space straight k space dt space Now comma space on space integrating space both space sides comma space integral subscript straight v subscript straight o end subscript superscript straight v dv over straight v space equals space minus space straight k integral subscript 0 superscript straight t dt space rightwards double arrow space Ln space straight v vertical line subscript straight v subscript straight o end subscript superscript straight v space equals space minus kt vertical line subscript 0 superscript straight t space rightwards double arrow Ln space straight v over straight v subscript straight o space equals space minus space kt space rightwards double arrow space straight v space equals space straight v subscript straight o space straight e to the power of negative kt end exponent$

Some More Questions From Motion in Straight Line Chapter

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.

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Motion In Straight Line

After the engine of a moving motorboat is cut off, the motorboat retards with retardation directly proportional to v. What is the magnitude of velocity at any instant after the engine is cut off, if the velocity at the time of cut off is v₀?

Some More Questions From Motion in Straight Line Chapter

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.

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Motion In Straight Line

After the engine of a moving motorboat is cut off, the motorboat retards with retardation directly proportional to v. What is the magnitude of velocity at any instant after the engine is cut off, if the velocity at the time of cut off is v0?

Some More Questions From Motion in Straight Line Chapter

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion: (a) A kite flying in the sky. (b) The earth revolving around the sun. (c) A train moving along the equator of the earth in clockwise direction. (d) Accelerated motion of a particle in a straight line.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

After the engine of a moving motorboat is cut off, the motorboat retards with retardation directly proportional to v. What is the magnitude of velocity at any instant after the engine is cut off, if the velocity at the time of cut off is v₀?

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.