Motion In Straight Line

Question

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The displacement x of a particle varies with time t as x = ae^-αt + be^βt where a, b, $α$ and β are positive constants. The velocity of the particle will

decrease with time

be independent of $α and β$

drop to zero when $α = β$

increase with time

Solution

increase with time

Given:-

x = a e^-αt + be^βt

We know that

velocity v = $\frac{dx}{dt}$

v = $\frac{d}{dt} ({ae}^{- αt} + {be}^{βt})$

= -a $α$ e^-αt + bβ e^βt

v = $- a {αe}^{- αt} + bβ e^{βt}$

v = A + B

where A = - a $α e^{- αt}$ , B = bβ e^-βt

The value ot term A = -a $α e^{- αt}$ increases and of term B = bβ e^-βt increases with time. As a result velocity goes on increasing with time.

Some More Questions From Motion in Straight Line Chapter

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

The displacement x of a particle varies with time t as x = ae^-αt + be^βt where a, b, $α$ and β are positive constants. The velocity of the particle will

decrease with time

be independent of $α and β$

drop to zero when $α = β$

increase with time

Some More Questions From Motion in Straight Line Chapter

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.

Define distance.

Define displacement.

Can magnitude of displacement be greater than distance travelled by particle?

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For Daily Free Study Material Join wiredfaculty

Motion In Straight Line

The displacement x of a particle varies with time t as x = ae-αt + beβt where a, b, α and β are positive constants. The velocity of the particle will decrease with time be independent of α and β drop to zero when α = β increase with time

Some More Questions From Motion in Straight Line Chapter

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.

Define distance.

Define displacement.

Can magnitude of displacement be greater than distance travelled by particle?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The displacement x of a particle varies with time t as x = ae^-αt + be^βt where a, b, $α$ and β are positive constants. The velocity of the particle will

decrease with time

be independent of $α and β$

drop to zero when $α = β$

increase with time

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.