- Introduction
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- Position and Displacement
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- Average velocity and speed
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- Instantaneous velocity and speed
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- Acceleration
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- Motion with constant acceleration
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- Free fall acceleration
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- Relative velocity
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- Solved Examples Part 1
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- Solved Examples Part 2
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- Solved Examples Part 3
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- Solved Examples Part 4
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- Solved Examples Part 5

- Position Distance and Displacement
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- Average velocity and speed
- |
- Velocity and acceleration
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- Uniformly accelerated motion
- |
- Relative Velocity
- |
- Kinematics Question 1
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- Kinematics Question 2

In this page we have *1D Kinematics Solved Examples* . Hope you like them and do not forget to like , social share
and comment at the end of the page.

**Question 17.**The displacement of a particle moving in straight line depends on time t as

x=at^{3}+bt^{2}+ct+d

which of the follwing is true

a. Intial acceleration depends on b only

b Intial velocity depends on c only

c. Intial displacement is d

d. Ratio of intial velocity /intial acceleration depends on a and c

**Solution(17)**:

. The displacement of a particle moving in straight line depends on time t as

x=at^{3}+bt^{2}+ct+d

Velocity (dx/dt)=3at^{2}+2bt+c

Acceleration (d^{2}x/dt^{2})=6at+2b

So Intial displacement(t=0) =d

Intial velolcity(t=0) =c

Intial acceleration (t=0) =2b

**Question 18.**A particle located at x=0 at time t=0 starts moving along the positive x-direction with a velocity v that varies as

v=√x

The displacement of the particles varies with time as

which of the follwing is true

a. t^{2}

b t^{3}

c. t^{4}

d. t^{1/2}

**Solution(18)**:

. Given v=√x

or

dx/dt=√x

dx/√x=dt

Integrating both sides between the limit (0,x) and (0,t)

x=t^{2}/4

Hence (a) is correct

**Question 19.**A Train is moving along a straight section of the track with a velocity of 180km/h. The braking deceleration is 2m/s^{2}s

At what distance from a train station should the train driver aply the brake so that train stops at the station

a. 800m

b 625m

c. 700m

d. none of these

**Solution(19)**:

. we are given

v_{0}=180km/h=50m/s

a=-2m/s^{2}

Now v^{2}=v_{0}^{2}+2as

0=(50)^{2}-2*2*x
or x=625m
hence (b) is correct
**Question 20.**from the previous question,how long will it take to bring the train to the halt

a. 25s

b 20s

c. 15s

d. none of these

**Solution(20)**:

. Now v=v_{0}+at

0=50-2t

or t=25 sec

Hence (a) is correct

**More Practice Questions**

**Question 1** A car brakes from a speed of 108 km/h to 72 km/h duing a displacement of 100m. What is its acceleration?

**Solution** This can be easily found using Third Kinematics equations

v^{2}=u^{2}+2as

a=-2.5 m/s^{2}

**Question 2** A Ball is dropped from a building of the height 90 m . Simultanously another ball is thrown up with a speed of 40 m/s. Calculate the Relative speed of the balls as a function of time?

**Solution**

Both the balls are falling freely under gravity .Therefore no acceleration of one with respect to other .So relative speed of the balls remains constant equal to 40m/s

**Question 3**

The Relation between t and distance x is given by

t=ax^{2} +bx where a and b are constant.

Expreess instaneous acceleration in terms of instaneous velocity

**Solution**

acceleration =-2av^{3}

**Question 4** A car travels 100 km in 2 hours and 50 km in 1 hour in the same direction.

a) What is the Car's average speed for the whole journey?

b) What is the Car's average velocity for the whole journey?

**Solution**

50km/h,50km/h

**Question 5**

Two balls of different masses (one lighter and other heavier) are thrown vertically upwards; with the same speed. Which one will pass through the point of projection in their downward direction with the greater speed?

**Solution**

In case of motion under gravity, the speed with which a body returns back is always equal to the speed with which it is thrown up. Since expression for final speed does not involve mass, both the balls will acquire the same speed.

Go Back to Class 11 Maths Home page Go Back to Class 11 Physics Home page

#### Recommended Physics books for class 11

x=at

which of the follwing is true

a. Intial acceleration depends on b only

b Intial velocity depends on c only

c. Intial displacement is d

d. Ratio of intial velocity /intial acceleration depends on a and c

. The displacement of a particle moving in straight line depends on time t as

x=at

Velocity (dx/dt)=3at

Acceleration (d

So Intial displacement(t=0) =d

Intial velolcity(t=0) =c

Intial acceleration (t=0) =2b

v=√x

The displacement of the particles varies with time as

which of the follwing is true

a. t

b t

c. t

d. t

. Given v=√x

or

dx/dt=√x

dx/√x=dt

Integrating both sides between the limit (0,x) and (0,t)

x=t

Hence (a) is correct

At what distance from a train station should the train driver aply the brake so that train stops at the station

a. 800m

b 625m

c. 700m

d. none of these

. we are given

v

a=-2m/s

Now v

0=(50)

a. 25s

b 20s

c. 15s

d. none of these

. Now v=v

0=50-2t

or t=25 sec

Hence (a) is correct

v

a=-2.5 m/s

Both the balls are falling freely under gravity .Therefore no acceleration of one with respect to other .So relative speed of the balls remains constant equal to 40m/s

The Relation between t and distance x is given by

t=ax

Expreess instaneous acceleration in terms of instaneous velocity

acceleration =-2av

a) What is the Car's average speed for the whole journey?

b) What is the Car's average velocity for the whole journey?

50km/h,50km/h

Two balls of different masses (one lighter and other heavier) are thrown vertically upwards; with the same speed. Which one will pass through the point of projection in their downward direction with the greater speed?

In case of motion under gravity, the speed with which a body returns back is always equal to the speed with which it is thrown up. Since expression for final speed does not involve mass, both the balls will acquire the same speed.

Go Back to Class 11 Maths Home page Go Back to Class 11 Physics Home page

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