CBSE PHYSICS class 9th Motion Numerical Problems

1. An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff. 2. A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car. 3. Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far will he fall? 4. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled. 5. A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s2. Determine the time for the feather to fall to the surface of the moon. 6. Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of 444 m/s in 1.8 seconds, then what is the acceleration and what is the distance that the sled travels? 7. A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike. 8. An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s2. The takeoff speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway? 9. A car traveling at 22.4 m/s skids to a stop in 2.55 s. Determine the skidding distance of the car (assume uniform acceleration). 10. A kangaroo is capable of jumping to a height of 2.62 m. Determine the takeoff speed of the kangaroo. 11. If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed and his hang time (total time to move upwards to the peak and then return to the ground)? 12. A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.840 m. Determine the acceleration of the bullet (assume a uniform acceleration). 13. A baseball is popped straight up into the air and has a hang-time of 6.25 s. Determine the height to which the ball rises before it reaches its peak. (Hint: the time to rise to the peak is one-half the total hang-time.) 14. The observation deck of tall skyscraper 370 m above the street. Determine the time required for a penny to free fall from the deck to the street below. 15. A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The bullet penetrates for a distance of 0.0621 m. Determine the acceleration of the bullet while moving into the clay. (Assume a uniform acceleration.) 16. A stone is dropped into a deep well and is heard to hit the water 3.41 s after being dropped. Determine the depth of the well. 17. It was once recorded that a Jaguar left skid marks that were 290 m in length. Assuming that the Jaguar skidded to a stop with a constant acceleration of -3.90 m/s2, determine the speed of the Jaguar before it began to skid. 18. A plane has a takeoff speed of 88.3 m/s and requires 1365 m to reach that speed. Determine the acceleration of the plane and the time required to reach this speed. 19. A dragster accelerates to a speed of 112 m/s over a distance of 398 m. Determine the acceleration (assume uniform) of the dragster. 20. With what speed in miles/hr (1 m/s = 2.23 mi/hr) must an object be thrown to reach a height of 91.5 m (equivalent to one football field)? Assume negligible air resistance. Solutions 1. . d = 1720 m 2. a = 8.10 m/ s2 3. V = -25.5 m/s (- indicates direction) 4. a = 11.2 m/s2 , d = 79.8 m 5. t = 1.29 s 6. a = 247 m/s2 7. d = 400 m 8. a = 0.712 m/s2 9. d = 704 m 10. d = 28.6 m 11. vi = 7.17 m/s 12. vi = 5.03 m/s 13. hang time = 1.03 s 14. a = 1.62*105 m /s2 15. vi = 30.6 m/s , d = 47.9 m 16. t = 8.69 s 17. a = -1.08*106 m /s2 18. d = -57.0 m 19. vi = 47.6 m /s 20. a = 2.86 m/s2 21. t = 30. 8 sa = 15.8 m/s2 22. vi = 42.3 m/s , vi = 94.4 mi/hr

IX Motion And Rest Formative Check Points For FA-01

Circular Motion CBSE Class 9th 

Q.What is circular motion.Is circular motion  an acceleration motion?

Motion of a  body  along a circle (circular path), is called a circular motion. Circular motion is an acceleration motion because velocity changes due to the change in the direction of motion.

When an object moves in a circular path with uniform speed, its motion is called uniform circular motion.

Q. Take a piece of thread and tie a small piece of stone at one of its ends. Move the stone with constant speed by holding the thread at the other end. What will be the direction in which the stone moves after it is released.

Answer: If we releas the thread , the stone moves along a straight line tangential to the circular path. This is because once the stone is released, it continues to move along the direction it has been moving at that instant.

Q. Define terms (i) One radian (ii)  Angular displacement (iii) Angular velocity

Answer: One radian is defined as the angle subtended at the centre of the circle by an arc equal in length to its radius.

Angular displacement : In a circular motion, the angular displacement of a body is the angle subtended by the body at the centre in a given interval of time. It is represented by the symbol q (theta).                              

Angular velocity : The angular displacement per unit time is called the angular velocity. it is represented by the symbol w(omega).

Angular velocity w = q/t

In figure, the arc AB of the circle has length l  and subtends an angle q at the centre C.

 If q radians.

Then, q = l /r radians

[For l  = 1, q = 1 radian] 

Angle subtended by the circumference at the centre, q = 2pr/r =2p radian

For complete circle at centre 2p radian = 360⁰

1 radian =  (360⁰/2p) =57.3⁰

Q. Determine relation between linear velocity and Angular velocity.

Ans: Consider a body moving along the circumference of a circle of radius r with linear velocity v. Its angular velocity is ω.

Let the body moves from A to B in a time t and ө is the angle covered 

 

Let AB = S = displacement

Linear velocity = displacement / time

v = AB/t

v= St  …………(1)

If ө is the angle subtended by an arc of length s and radius r. Then  S = r ө …………(2)

Substituting (2) in (1),

v = r ө/t

But ө/t = ω = angular velocity

v = r ω

Linear velocity = Radius of the circle x Angular velocity

Q. What do you mean by centripetal force and centrifugal force?

Answer: The constant force that acts on the body along the radius towards the centre and perpendicular to the velocity of the body is known as centripetal force.

Let us consider an object of mass m, moving along a circular path of radius r, with an angular velocity ω and linear velocity v.

F = (mv²)/r

Again, centripetal force, F = mrω²     [( since v = rω )

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IX Motion And Rest Formative Check Points

IX Physics force motion problems Numerals On Google Search

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Practice Questions Based on CBSE Physics class IX Chapter Motion and Rest

CCE Physics IX Chapter based Formative and Summative Assessments

1. A jogger runs with a constant 2.2 m/s speed for 15 minutes. What distance does she travel during that time?

2. After 15 minutes, the jogger in problem 1 gets tired, and during the next 2 seconds, she reduces her speed to 1.8 m/s. What was her average acceleration during these 2 seconds?

3. Assuming she moves during these 5 seconds with an average speed of 2.0 m/s, what distance does she travel while decelerating?

4. Add the results in problems 1 and 3, and using the total time of the motion, 15 minutes and 5 seconds, find the overall average speed of the jogger.

5. What is the acceleration of a tennis ball if initially it comes toward the player's racquet at 20 m/s, and it leaves in the opposite direction at 24 m/s? A high-speed camera indicates the time of impact of 4.0m s.

6. How long does it take the ball in problem 5 to travel 15 meters after being played? Neglect the gravitational effect, and suppose the ball travels along a straight line and assume a speed of 24 m/s

Practice Questions and Numerical Motion and Rest

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9th CBSE physics chapter motion and rest merit gainer series

Motion And Rest Physics Class IX

CBSE chapter-wise MCQ Multiple Choice Questions,Test Paper,Sample paper on CCE pattern for class 9 science Motion. Distance and displacement, velocity; uniform and non-uniform motion along a straight line; acceleration, distance-time and velocity-time graphs for uniform motion and uniformly accelerated motion, equations of motion by graphical method; elementary idea of uniform circular motion.
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CBSE PHYSICS class 9th Motion Numerical Problems unsolved

CBSE- PHYSICS- IX- MOTION AND REST STUDY NOTES

A body is said to be in the state of rest when it remains in the same position with respect to time.
e.g.: The position of trees around the building is not changing with respect to the building. Then the trees are at rest.

A body is said to be in the state of motion, when it continuously changes its position with respect to time
e.g.: When we are cycling or running, we are changing position with respect to trees and buildings. we are said to be moving
DISTANCE AND DISPLACEMENT

Distance is the length of the path covered by a body. It has no sense of direction so it is a scalar quantity. Its SI unit of measurement is meter or m
The distance between the two places is not the same; it depends upon the path chosen.

Displacement:

The shortest distance, or distance travelled along a straight line, is known as displacement.If we draw a semicircle of radius 10cm. Then,
Displacement = r + r = 20cm
Distance = 2pr/2 = 10 x 22/7 cm = 31.4cm

UNIFORM MOTION AND NON UNIFORM MOTION

If an object covers equal distances in equal intervals of time, it is said to be in uniform motion.
If an object covers unequal distance in equal intervals of time, it is said to be in non-uniform motion.

MEASURING THE RATE OF MOTION

Speed :It is the distance travelled in one second (or) rate of distance travelled.

A car starts from Samastipur and reaches Patna in 6 hour. A bus takes 8 hour to travel the same distance. Which has moved faster? Why?

The car travels faster than the bus, because it covers the distance in a short time.

When a body covers a distance in a short time, it is said to be fast. If it takes more time to cover the distance, it is said to be slow.

Hence, Speed is the quantity used to say whether the motion is slow or fast.

Speed = Total Distance travelled/ Time taken
Speed has no sense of the direction of motion so it is a scalar quantity
SI Units: Speed is measured in m/s (or) m/s It can also be expressed in km/hour (or) kmh-1

Velocity : The speed with direction is known as velocity. So to measure the velocity, you should consider displacement instead of distance.Velocity is the displacement made in one second (or) rate of change of displacement. Rate of change means, change per second.

Velocity = Displacement/Time
It S. I.    Unit is also m/s

Uniform Velocity: Equal displacement covered by a body in equal intervals of time is known as uniform velocity.
Acceleration is the change in velocity of an object per second or rate of change of velocity.
Acceleration = Change in velocity/Time taken. The unit of acceleration is m/s2 or ms-2

There are two cases of of change of velocity
If the velocity of the body increases with time, the acceleration is positive, and the kind of motion is called accelerated motion.
If the velocity of the body decreases with time, the acceleration is negative (retardation), and the motion is called decelerated motion.

Uniform Acceleration: If an object travels in a straight line and its velocity increases or decreases by equal amount in equal intervals of time, then the acceleration of the object is uniform.

We can derive a formula for acceleration.
a= [v – u] / t

Where u - initial velocity, v - final velocity t – time

Distance - time graph

We can easily understand the relation between time and distance by using a graph.

Taking a suitable scale, a graph is drawn bytaking time along the x axis and distance along the y axis. The graph is known as distance – time graph.
In the graph for uniform speed is a straight line and curved for Non uniform speed.

Physics Ch: Motion and Rest -Practice paper and Numerical For SA-I

Physics IX(9th) Ch: Motion and Rest Numerical Paper For SA-I

1)   Calculate the average speed of a train, which covers 120 km in 2 hours.Distance covered by the train = 120 km

2)   .How far does a car travel in 2.5 h if its average speed is 60 km/h ?

3)   .A carriage moves 30 km in one hour. Calculate its speed in m/s. Is it average or uniform speed?

4)   You are asked to run in a straight line. If you cover a distance of 5 m in each second, what is your (a) speed (b) velocity?

5)   Draw the velocity time graph of a body moving with uniform velocity of 5m/s.

6)   Write the equation of motion connecting S, u, v and a where the symbols have their usual meanings.

7)   What do you infer, if the distance-time graph is a straight line?

8)   The distance (S) in meters traveled by a particle is related to time(t) in seconds by the equation of motion . What is the initial velocity of the particle?

9)   .On a 60 km track, a train travels the first 30 km at a uniform speed of 30 km/h. How fast must the train travel the next 30 km so that the average speed is 40 km/h for the entire trip?

10)  A train travels a distance with a speed of 30 km/h and returns with a speed of 50 km/h. Calculate the average speed of the train.

11)  Which one of the three is having maximum and the least average speed?1) Bicycle moving with 12 km/h    2) A man running with 5m/s  3) A car moving with 1500 m/min.

12)  A car moving with an initial velocity of 25 m/s is brought to rest in 20 seconds. Calculate the acceleration.

13)  A car, which was at rest, attains a speed of 90 km/h in 10 seconds. Calculate the acceleration.

14)  A body starts from rest and moves with a uniform acceleration of 2m/s2. What will be its velocity and displacement at the end of 10 seconds?

15)  A body moves with an initial velocity of 2 m/s and uniform acceleration of 3m/s2. Calculate the velocity when it has traveled a distance of 84 meters.

16)  Calculate the distance traveled in 10 seconds by an object Time (t) = 10 seconds

17)  Question 20.A ball starting from rest slides down an inclined plane of length 10 m with a speed of 10 m/s. What is the acceleration produced in the ball?

18)  A ship is moving at a speed of 56 km/h. One second later it is moving at 58 km/h. What is its acceleration?

19)  A car traveling at 20 km/h speeds up to 60 km/h in 6 seconds. What is its acceleration?

20)  What is the distance covered by a bus starting from rest and moving with a uniform acceleration of 1 m/s2 for 120 seconds?

21)  Find the initial velocity of a train, which is stopped in 25 seconds. The retardation produced in the train is 1.5 m/s2.

22)  A car travels 30 km at a uniform speed of 40 km/h and the next 30 km at a uniform speed of 20 km/h. Find its average speed.

23)  A car is moving with a uniform acceleration for the first ten seconds and then it moves with a uniform velocity of 30 m/s for the next ten seconds. The brakes are applied and the car comes to rest with a uniform acceleration in 5 seconds. Draw a v-t graph to show the nature of motion. How far does the car travel after the brakes are applied?

24)  Plot a displacement-time graph for the given data and calculate the speed (a) at the end of 5 seconds (b) in the next two seconds (c) in the last two seconds.

25)  A car is traveling at 54 km/h. If brakes are applied so as to produce uniform retardation of 5m/s2. Calculate the time taken by it to stop.

26)  A driver of a car A traveling at a uniform speed of 54 km/h for 10 secs applies the brakes and decelerates uniformly. The car stops in 5 seconds. Driver of car B going at 36 km/h for 10 sec applies the brakes slowly and stops after 10 seconds. Plot the speed-time graph of both cars and find out which of the two cars traveled further after the brakes were applied.

27)  What is the average speed of a car which covers half the distance with a speed of 20m/s and other half with a speed of 30m/s?