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A particle starts from the origin at time $t = 0$ and moves along the positive $x$ -axis. The graph of velocity with respect to time is shown in the figure. What is the position of the particle at time $t = 5 s$ ?

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Important Questions on Kinematics

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 3>Q 18

The distance

x

covered by a particle in one-dimensional motion varies with time

t

x^{2} = a t^{2} + 2 b t + c

. If the acceleration of the particle depends on

x

x^{- n},

where

n

is an integer, the value of

n

is-

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 3>Q 19

A particle starts from the origin at

t = 0

with an initial velocity of

3.0 \hat{i} m s^{- 1}

and moves in the

x - y

plane with a constant acceleration

(6.0 \hat{i} + 4.0 \hat{j}) m s^{- 2}

. The

x

-coordinate of the particle at the instant when its

y

-coordinate is

32 m

D

meters. The value of

D

is:

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 3>Q 21

Two stones are thrown up simultaneously from the edge of a cliff

240 m

high with an initial speed of

10 m s^{- 1}

and

40 m s^{- 1}

, respectively. Which of the following graph best represents the time variation of the relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take

g = 10 m s^{- 2}

) (The figures are schematic and not drawn scale).

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 3>Q 22

The ship

A

is sailing towards the northeast with velocity

\vec{v} = (30 \hat{i} + 50 \hat{j}) km h^{- 1}

, where

\hat{i}

points east and

\hat{j}

points north. The ship

B

is at a distance of

80 km

east and

150 km

north of the ship

A

and is sailing towards the west at

10 km h^{- 1}

A

will be at a minimum distance from

B

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 3>Q 23

A particle is moving along the

x -

axis with its coordinate as a function of time

t

given by,

x (t) = (10 + 8 t - 3 t^{2}) m

. Another particle is moving along the

y -

axis with its coordinate as a function of time given by,

y (t) = (5 - 8 t^{3}) m

. At

t = 1 s

, the speed of the second particle as measured in the frame of the first particle is given as

\sqrt{v}

. Then

v (in m s^{- 1})

is,

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 3>Q 24

Consider a body of mass

1.0 kg

at rest at the origin at time

t = 0 .

A force

\vec{F} = (α t \hat{i} + β \hat{j})

is applied on the body, where

α = 1.0 {Ns}^{- 1} and β = 1.0 N .

The torque acting on the body about the origin at time

t = 1.0 s

\vec{τ}

. Which of the following statements is (are) true?

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 3>Q 25

Small particle of mass $m$ is projected at an angle $θ$ with the $x -$ axis with an initial velocity $v_{0}$ in the $x - y$ plane as shown in the figure. At a time $t < \frac{v_{0} sinθ}{g}$ the angular momentum of the particle is

Question Image

where $\hat{i}, \hat{j}$ and $\hat{k}$ are unit vectors along $x, y$ and $z -$ axis respectively.

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 4>Q 1

A projectile aimed at a mark which is in the horizontal plane through the point of projection falls

a cm

short of it when the elevation is

α

and goes

b cm

too far when the elevation is

β .

Show that if the velocity of projection is same in all the case, the proper elevation is

\frac{1}{2} \sin^{- 1} [\frac{b \sin 2 α + a \sin 2 β}{a + b}]

A particle starts from the origin at time t=0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in the figure. What is the position of the particle at time t=5 s?

Important Questions on Kinematics

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A particle starts from the origin at time $t = 0$ and moves along the positive $x$ -axis. The graph of velocity with respect to time is shown in the figure. What is the position of the particle at time $t = 5 s$ ?