- distance and displacement
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- Velocity and speed
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- Instantaneous velocity and speed
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- Acceleration
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- Kinematic equations for uniformly accelerated Motion
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- Free fall acceleration
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- Relative velocity
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- Kinematics Sample Problems and Solutions
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- One dimensional motion problems with solution
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- Motion graphs worksheet with Answer

- Important Questions on Kinematics
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- Kinematics worksheet
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- Motion in one dimension Practice Paper
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- Acceleration worksheet with answers

A particle moves in a straight line according to the relation

$x=t^3-4t^2+3t$

Find the acceleration of the particle at displacement equal to zero.

a. (-8,-2,10)

b. (-1,-2,10)

c. (8,2,10)

d. (1,2,10)

Solution

A body starts at initial velocity $v_0$ in a straight line with acceleration as shown below in the graph.

Find the maximum velocity reached.

a. $v_0+4at_0$

b. $v_0+ \frac {9}{2}(at_0)$

c. $v_0 - \frac {9}{2}(at_0)$

d. $v_0 - 4at_0$

Solution

A particle moves in a straight line with acceleration described by equation given below

$a=mx- \frac {v_{0}^{2}}{x_0}$

If the initial velocity and displacement are $(v_0, 0)$ and at any time $t_0$ velocity and displacement are $(0, x_0)$ the value of constant m is

Solution

A boat moves with the stream of water from point A and B and it return back with the same speed. Velocity of boat relative to water is $\eta$ times the velocity of the water. Velocity of the water is 1m/sec. Find out the average speed in the whole iternary

Solution

A body is freely falling under the action of gravity. It covers half the total distance in the last second of its fall. If it falls for n second, then value of n is

a. $2$

b. $2 + \sqrt {2}$

c. $3$

d. $2 - \sqrt {2}$

Solution

Two particle A and B start with the same velocity $v=v_0$ at x=0.They are accelerated per the graph shown above. Which particle has the maximum magnitude of the velocity at $x=x_0$

a. A

b. B

c. A & B will have same velocity

d. None of the above

Solution

Distance and displacement of a moving object have same magnitude when

a. When object moves in circular motion

b. When object moves along a zig-zag path

c. When object moves along straight line and always moves along the same direction

d. When it moves along straight line but the distance is not always same

Solution

The greatest possible acceleration or deceleration a train may have is a and its maximum speed is v. Find the maximum time in which the train can get from one station to the next if the total distance is s

Solution

Displacement(y) of the particle is given by

$y=2t+t^2-2t^3$

the velocity of the particle when acceleration is zero is given by

a. $\frac {5}{2}$

b. $ \frac {9}{4}$

c. $ \frac {13}{6}$

d. $ \frac {17}{8}$

Solution

A particle is set in motion at t=0 such that velocity varies as $v= v_0(1 - \frac {t}{2})$ where $v_0$ is a positive constant. Find the distance, displacement covered by the particle in first 3 sec

Solution

The velocity, displacement, acceleration of a particle in one dimensional motion is given as

$v_1,x_1,a_1 $ at $t=t_0$

$v_2,x_2,a_2 $ at $t=t_0 + \Delta t$

which of the following is correct

Solution

The displacement time equation for a particle in linear motion is given as

which of the following option is correct

a. The velocity and acceleration of the particle at t=0 is $a$ and $-ab$ respectively

b. The velocity will be decreasing as the time increases

c. The displacement of the particle will fall between

d. The maximum acceleration in the motion is $-ab$

Solution

Consider the figure given below

a.Acceleration is positive during A to C and negative during C to B

b.Acceleration is maximum at C

c.Velocity is maximum at C

d. Average acceleration is zero during the journey

Solution

Which one of the following statement(s) is true?

a.A body moving with uniform speed can have variable velocity

b.A body moving with uniform velocity can have variable speed

c.Average velocity is always equal to instantaneous velocity

d.x-t graph can be a straight line parallel to position axis

Solution

Which one of the following statement is correct?

a. A body has constant speed but varying velocity

b. A body has constant speed but varying acceleration

c. A body having constant speed cannot have acceleration

d. None of the above

Solution

A body moves along a semicircular track of Radius R. Which of the following statement is true

a. Displacement of the body is $2R$

b. Distance travelled by the body is $\pi R$

c. Displacement of the body is $\pi R$

d. none of the above

Solution

Which of the following is false

a. The speed of the particle at any instant is given by the slope of the displacement-time graph

b. The distance moved by the particle in a time interval from t

c. Magnitude of the acceleration of the particle at any instant is given by the slope of the velocity time graph

d. none of the above

Solution

A particle is going moving along x-axis. Which of the following statement is false

a. At time t

b. At time t

c. If the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval.

d. At time t

Solution

A particle starts at time t=0 from x=0 along the positive x-axis with constant speed v .After time t,it return back towards the origin with the speed 2v and reaches the origin in t/2 sec .Which of the following is true for the whole process

a. Average velocity is zero for the whole process

b. Average speed is $\frac {4v}{3}$ for the whole process

c. Displacement at time t is equal to vt d. Displacement at time $ \frac {3t}{2}$ is $2vt$

Solution

A car, starting from rest is accelerated at constant rate a until it attains speed v. It is then retarded at a constant rate b until it comes to rest. which of the following is true

a. the average speed for the whole motion is $ \frac {av}{2b}$

b. the average speed for the whole motion is $ \frac {v}{2}$

c. Total time taken for the journey is $ v(\frac {1}{a}+\frac {1}{b})$

d. none of the above

Solution

Find the position, velocity of the stone as seen by the Man X at time t=2 sec

a. (19m ,19m/s)

b. (19.6m,19.6m/s)

c. (10m,10m/s)

d (11m,12m/s)

Solution

Find the position, velocity of the stone relative to Man Y at 3 sec

a. (39m, 70m/s)

b. (19m, 70m/s)

c. (70m, 39 m/s)

d. (14 m, 29m/s)

Solution

Find the acceleration of the stone with respect to Man X and Y.

a. (9.8 m/s

b. (9 m/s

c. (10 m/s

d. None of these

Solution

Bullet one is fired in the north direction with the muzzle velocity $u$. Find the velocity of the bullet as seen from the observer on the earth

a. $u+v$

b. $u-v$

c. $u$

d. $v$

Solution

Find the velocity of the bullet as seen from the observer on the moving car

a. $u+v-w$

b. $u-v-w$

c. $u$

d. $v$

Solution

Bullet one is fired in the south direction with the muzzle velocity u. Find the velocity of the bullet as seen from the observer on the earth

a. $u+v$

b. $v-u$

c. $u$

d. $v$

Solution

Find the velocity of the second bullet as seen from the observer on the moving car

a. u+v-w

b. v-u-w

c. u

d. v

Solution

Velocity of train relative to its driver

a. 0

b. 15 m/s

c. -15 m/s

d. 20 m/s

Solution

What is the velocity of train with respect to monkey

a. 5m/s

b -5 m/s

c. 15 m/s

d -15 m/s

Solution

Find the velocty of ground with respect to monkey

a. 5 m/s

b. -5 m/s

c. 10 m/s

d. -10 m/s

Solution

Water drips from a faucet at a uniform rate of m drops per second. Find the distance x between the two adjacent drops as a function of time t that the trailing drop has been in motion.

a. $x = g\frac {t}{m} + g \frac {1}{2m^2}$

b. $x = g \frac {1}{2m^2}$

c. $x = g \frac {1}{4m^2}$

d. $x=g\frac {t}{2m} + g \frac {1}{2m^2}$

Solution

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