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$Y$ component of velocity is $20$ and $X$ component of velocity is $10$ . The direction of motion of the body with the horizontal at this instant is

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Important Questions on Dynamics

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A car covers the first half distance between two places at

40 kmph

and the other half at

60 kmph .

The average speed of the car is

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

The displacement-time graphs of two moving particles make angles of $30 °$ and $45 °$ with the $x$ -axis as shown in the figure. The ratio of their respective velocity is:

Question Image

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A particle shows the distance-time curve as shown in the figure. The maximum instantaneous velocity of the particle is around the point.

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EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

In $1.0 s,$ a particle goes from $A to B$ moving in a semicircle of $1.0 m$ radius (as shown in the figure)

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The magnitude of the average velocity is

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

The displacement of a body is given by

x = 4 t + 5 t^{3},

where

x

is in metre and

t

is in second. The difference between the average velocity of the body in the time-interval

t = 1 s

t = 2 s

and its instantaneous-velocity at

t = 1 s

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A body covers one-third of the distance with a velocity

v_{1},

the second one-third of the distance with a velocity

v_{2}

and the last one-third of the distance with a velocity

v_{3}

. The average velocity is

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A particle is projected from the ground with an initial speed of

v

at an angle

θ

with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

Among the four graphs given below, there is only one graph for which average velocity over the time interval

(0, T)

can vanish for a suitably chosen

T

. Which one is it?

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A person travelling on a straight line moves with a uniform velocity

v_{1}

for some time and with uniform velocity

v_{2}

for the next equal time. The average velocity

v

is given by

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A man walks

6.5 km

East in

2 hours

and then

2.5 km

West in

1 hour

. Calculate the man's average velocity for the whole journey.

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A body starts from rest and moves with a constant acceleration. The ratio of distance covered in the

n

th second to the distance covered in

n

second is

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A stone is projected with a velocity

20 \sqrt{2} m s^{- 1}

at an angle of

45 °

to the horizontal. The average velocity of stone during its motion from starting point to its maximum height is

(g = 10 m s^{- 2})

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A point moves with uniform acceleration and

v_{1}, v_{2}

and

v_{3}

denote the average velocities in the three successive intervals of time

t_{1}, t_{2}

and

t_{3}

. Which of the following relations is correct?

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A point initially at rest moves along

x

-axis. Its acceleration varies with time as

a = (6 t + 5)

m s^{- 2}

. It starts from origin, the distance covered in 1 s is

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A pigeon is flying between two cars moving towards each other on a straight road. The first car is moving with a speed of

27 k m h^{- 1}

while the other car is moving with a speed of

18 k m h^{- 1}

. The pigeon starts moving from the first car towards the other and is moving with a speed of

36 k m h^{1}

when the two cars were separated by

36 k m .

Now, find the total distance travelled by the pigeon:

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

The following figure shows

x - t

graph of a particle. Find the time

t

such that the average velocity of the particle during the period

0

t

is zero.

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A particle moves along a straight line and its velocity depends on time as

v = (4 t - t^{2}) m s^{- 1}

. Then, for first

5 s

EASY

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

A particle moves for 20 s with velocity

3 {m s}^{- 1}

and then moves with velocity

4 {m s}^{- 1}

for another 20 s and finally moves with velocity

5 {m s}^{- 1}

for next 20 s. What is the average velocity of the particle?

HARD

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

Assuming that the petrol burnt in a motorboat varies as the cube of its velocity, the most economical speed when going against a current of

c

km per hour is

MEDIUM

Mathematics>Statics and Dynamics>Dynamics>Uniform Motion and Its Equation

The velocity-time graph of a particle moving along a straight line is as shown in diagram. The rate of acceleration and retardation is constant and is equal to $5 m s^{- 2}$ . If the average velocity during the motion is $20 m s^{- 1}$ , then
Question Image
The value of t is

Y component of velocity is 20 and X component of velocity is 10. The direction of motion of the body with the horizontal at this instant is

Important Questions on Dynamics

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$Y$ component of velocity is $20$ and $X$ component of velocity is $10$ . The direction of motion of the body with the horizontal at this instant is