Motion In Straight Line

Question

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A police party is moving in a jeep at a constant speed v. They saw a thief at a distance x on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a. Which of the following relations is true if the police is able to catch the thief?

$v^{2} < α x$

$v^{2} < 2 α x$

$v^{2} \geq 2 α x$

$v^{2} = αx$

Solution

$v^{2} \geq 2 α x$

Let the police party catch the thief after t

Distance travelled by police party in t = v t

and distance travelled by thief = $x + \frac{1}{2} α t^{2}$

⇒ $x + \frac{1}{2} α t^{2} \leq v t$

⇒ $\frac{α t^{2}}{2} - vt + x = 0$

Since by using the Quadratic equation formula

$x = \frac{- b \pm \sqrt{b^{2} - 4 ac}}{2 a}$

⇒ $t = \frac{- (- v) \pm \sqrt{v^{2} - 2 \frac{α}{2} \times x}}{2 \times \frac{α}{2}}$

⇒ $t = \frac{v \pm \sqrt{v^{2} - 2 α x}}{α}$

Some More Questions From Motion in Straight Line Chapter

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

Some More Questions From Motion in Straight Line Chapter

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?

A body is thrown with a velocity of 9.8 m/s in the vertical upward direction. What is the velocity after one second?

How does the displacement of a particle change, when reference point for the position is shifted?

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Motion In Straight Line

Some More Questions From Motion in Straight Line Chapter

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?

A body is thrown with a velocity of 9.8 m/s in the vertical upward direction. What is the velocity after one second?

How does the displacement of a particle change, when reference point for the position is shifted?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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.