Motion in A Straight Line Test

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Consider a particle moving along the $$x$$-axis as shown in Fig. 4.138. Its distance from the origin O is described by the coordinate $$x$$ which varies with time. At a time $$t_1,$$ the particle is at point P, where its coordinate is $$x_2$$. The displacement during the time interval from $$t_1$$ and $$t_2$$ is the vector from P to Q the $$x$$-component of this vector is $$(x_2-x_1)$$ and all other component are zero.
It is convenient to represent the quantity $$x_2-x_1$$, the change in $$x$$, by means of a notation using the Greek letter $$\triangle $$ (capital delta) to designate a change in any quantity. Thus we write $$\triangle x=x_2-x_1$$ in which $$\triangle x$$ is not a product but is to be interpreted as a single symbol representing the change in the quantity $$x$$. Similarly, we denote the time interval from $$t_1$$ to $$t_2$$ as $$t=t_2-t_1.$$
The average velocity of the particle is defined as the ratio of the displacement $$\triangle x$$ to the time interval $$\triangle t$$. We represent average velocity by the letter v with a bar $$\left( \overline { v } \right) $$ to signify average value. Thus $$\overline { v } =\dfrac { x_{ 2 }-x_{ 1 } }{ t_{ 2 }-t_{ 1 } } =\dfrac { \triangle x }{ \triangle t } $$

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A particle moves half the time of its journey with velocity u. The rest of the half time it moves with two velocities $$v_1$$ and $$v_2$$ such that half the distance it covers with $$v_1$$ and the other half with $$v_2$$. Find the net average velocity assume straight line motion:

Motion in A Str...

Question 1

$$\dfrac { u\left( v_{ 1 }+v_{ 2 } \right) +2v_{ 1 }v_{ 2 } }{ 2\left( v_{ 1 }+v_{ 2 } \right) } $$

$$\dfrac { 2u\left( v_{ 1 }+v_{ 2 } \right) }{ 2u+v_{ 1 }+v_{ 2 } } $$

$$\dfrac { u\left( v_{ 1 }+v_{ 2 } \right) }{ 2v_{ 1 } } $$

$$\dfrac { 2v_{ 1 }v_{ 2 } }{ u+v_{ 1 }+v_{ 2 } } $$

Question 2

$$ 2\pi m $$

$$ (2\pi +40 m) $$

$$ 4\pi m $$

$$40 m$$

Question 3

1/3 s

8/3 s

1/5 s

8/5 s

Question 4

acceleration

momenta

potential energy

kinetic energy

Question 5

uniform acceleration

uniform speed

variable speed

variable acceleration

Question 6

$$ -10\, ms^{-1} $$

$$ 10\, ms^{-1} $$

$$ -20\, ms^{-1} $$

$$ 20\, ms^{-1} $$

Question 7

1 second

2 second

3 second

4 second

Question 8

a body at rest

a body in motion

a body neither at rest nor motion

none of these

Question 9

$$ 25 \,m $$

$$ 45\,m $$

$$ 90\,m $$

$$ 125\,m $$

Question 10

$$ 60\,m $$

$$ 55 \,m $$

$$ 25 \,m $$

$$ 30\,m $$

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