MOTION

 

 Motion (Class 9 - Science)

Worksheet 1

Section A: Multiple-Choice Questions (MCQs)

1. Which of the following is NOT a vector quantity?
   a) Velocity
   b) Speed
   c) Displacement
   d) Acceleration

2. A body is said to be in uniform motion when:
   a) It covers equal distances in equal time intervals
   b) Its speed keeps changing
   c) It moves along a circular path
   d) It is at rest

3. The slope of a velocity-time graph represents:
   a) Speed
   b) Acceleration
   c) Distance
   d) Displacement

4. A freely falling body has an acceleration due to gravity equal to:
   a) 8 m/s²
   b) 9.8 m/s²
   c) 10 m/s²
   d) 12 m/s²

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Section B: Fill in the Blanks

1. The SI unit of velocity is ____.
2. The area under a velocity-time graph represents ____.
3. If the acceleration of a body is zero, its velocity remains ____.
4. The motion of a pendulum is an example of ____.
5. Acceleration due to gravity is denoted by the letter ____.

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Section C: Short-Answer Questions

1. Define uniform and non-uniform motion with examples.
2. Differentiate between speed and velocity.
3. What do you mean by acceleration? What is its SI unit?
4. Explain why the motion of a car moving in a circular path at a constant speed is considered accelerated motion.
5. A bus starts from rest and attains a speed of 20 m/s in 10 seconds. Calculate its acceleration.

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Section D: Numerical Problems

1. A car moves with a uniform velocity of 72 km/h for 25 minutes. Find the distance traveled.
2. A cyclist increases his velocity from 10 m/s to 20 m/s in 5 seconds. Calculate his acceleration.
3. A stone is dropped from a height of 40 m. How long will it take to reach the ground? (Take g = 9.8 m/s²)
4. A train accelerates from 10 m/s to 30 m/s in 20 seconds. Find the acceleration and the distance covered.
5. A car moving with a speed of 30 m/s applies brakes and comes to rest in 5 seconds. Find the retardation and the distance covered before stopping.

Answers

Section A: Multiple-Choice Questions (MCQs)

1. (b) Speed
2. (a) It covers equal distances in equal time intervals
3. (b) Acceleration
4. (b) 9.8 m/s²

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Section B: Fill in the Blanks

1. The SI unit of velocity is m/s (meters per second).
2. The area under a velocity-time graph represents displacement.
3. If the acceleration of a body is zero, its velocity remains constant.
4. The motion of a pendulum is an example of periodic motion.
5. Acceleration due to gravity is denoted by the letter g.

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Section C: Short-Answer Questions

1. Uniform motion: A body is said to be in uniform motion when it covers equal distances in equal time intervals, e.g., a car moving at a constant speed on a straight road.
   Non-uniform motion: A body is in non-uniform motion if it covers unequal distances in equal time intervals, e.g., a car slowing down or speeding up.

2. Difference between speed and velocity:

   • Speed is the distance traveled per unit time and is a scalar quantity (e.g., 40 km/h).
   • Velocity is speed with direction and is a vector quantity (e.g., 40 km/h east).

3. Acceleration: The rate of change of velocity per unit time. Its SI unit is m/s².

4. A car moving in a circular path at a constant speed is considered to be in accelerated motion because the direction of velocity is continuously changing, even though its speed remains constant.

5. Acceleration Calculation:
   Given: Initial speed $u = 0$, Final speed $v = 20$m/s, Time $t = 10$ sec
   Acceleration $a = \frac{v - u}{t} = \frac{20 - 0}{10} = 2$ m/s²

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Section D: Numerical Problems

1. Distance Traveled
   Given: Speed $v = 72$ km/h, Time $t = 25$min
   Convert speed: $72 \times \frac{1000}{3600} = 20$m/s
   Convert time: $25 \times 60 = 1500$ sec
   Distance $s = v \times t = 20 \times 1500 = 30,000$m = 30 km

2. Acceleration Calculation
   Given: $u = 10$m/s, $v = 20$ m/s, $t=\mathrm{5<span\; style="font-family:\; verdana;">sec</span>}$$a = \frac{v - u}{t} = \frac{20 - 10}{5} = 2$ m/s²

3. Time to Reach the Ground
   Using the formula $h = \frac{1}{2} g t^2$
   Given: $h = 40$ m, $g = 9.8$m/s²
   $40 = \frac{1}{2} \times 9.8 \times t^2$
   $t^2 = \frac{40 \times 2}{9.8} = 8.16$
   $t = \sqrt{8.16} \approx 2.86$ sec

4. Acceleration and Distance
   Given: $u = 10$ m/s, $v = 30$ m/s, $t = 20$ sec
   $a = \frac{v - u}{t} = \frac{30 - 10}{20} = 1$m/s²
   Distance $s = ut + \frac{1}{2} a t^2$
   $s = 10(20) + \frac{1}{2} (1) (20)^2$
   $s = 200 + 200 = 400$m

5. Retardation and Distance
   Given: $u = 30$m/s, $v = 0$, $t = 5$ sec
   Retardation $a = \frac{v - u}{t} = \frac{0 - 30}{5} = -6$m/s²
   Distance $s = ut + \frac{1}{2} a t^2$
   $s = 30(5) + \frac{1}{2} (-6) (5)^2$
   $s = 150 - 75 = 75$ m

Worksheet 2

Section A: Multiple-Choice Questions (MCQs)

1. A particle is in uniform motion. Which of the following statements is true?
   a) Its acceleration is zero
   b) Its velocity changes continuously
   c) It covers unequal distances in equal time intervals
   d) Its speed keeps increasing

2. The acceleration of a body moving with uniform velocity is:
   a) Positive
   b) Negative
   c) Zero
   d) Cannot be determined

3. The area under a speed-time graph represents:
   a) Acceleration
   b) Velocity
   c) Distance traveled
   d) Displacement

4. A body moving in a straight line covers distances of 10 m, 20 m, and 30 m in consecutive seconds. The motion of the body is:
   a) Uniform
   b) Non-uniform
   c) Stationary
   d) None of the above

5. A car is moving with an initial speed of 10 m/s and comes to rest after covering a certain distance. If the deceleration is 2 m/s², what is the stopping distance?
   a) 25 m
   b) 30 m
   c) 20 m
   d) 15 m

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Section B: Fill in the Blanks

1. The SI unit of acceleration is ____.
2. If an object is moving along a straight line with constant speed, its acceleration is ____.
3. The slope of a distance-time graph represents ____.
4. A body moving with uniform acceleration has a constant change in ____.
5. The acceleration due to gravity is always directed towards ____.

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Section C: Short-Answer Questions

1. Differentiate between uniform acceleration and non-uniform acceleration with examples.
2. Explain why velocity is a vector quantity but speed is a scalar quantity.
3. Derive the equation of motion: $v = u + at$.
4. What is retardation? Give an example from daily life.
5. Explain why an object moving in a circular path at constant speed has acceleration.

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Section D: Numerical Problems

1. A car accelerates uniformly from 10 m/s to 25 m/s in 5 seconds. Find the acceleration.
2. A cyclist moves with a uniform speed of 18 km/h. Calculate the distance covered in 10 minutes.
3. A ball is thrown vertically upwards with a velocity of 20 m/s. Find the time taken to reach the highest point. (Take g = 9.8 m/s²)
4. A train moving at 20 m/s is brought to rest in 10 seconds. Find the acceleration and distance traveled before stopping.
5. A body starts from rest and moves with an acceleration of 4 m/s² for 5 seconds. Find the velocity attained and the distance covered.

Answers

Section A: Multiple-Choice Questions (MCQs)

1. (a) Its acceleration is zero
2. (c) Zero
3. (c) Distance traveled
4. (b) Non-uniform
5. (a) 25 m
   Using the formula $v^2 = u^2 + 2as$,
   Given: $v = 0$, $u = 10$m/s, $a = -2$m/s² $$0 = 10^2 + 2(-2)s$$
   $$0 = 100 - 4s$$
   $$s = 25 \text{ m}$$
   

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Section B: Fill in the Blanks

1. The SI unit of acceleration is m/s².
2. If an object is moving along a straight line with constant speed, its acceleration is zero.
3. The slope of a distance-time graph represents speed.
4. A body moving with uniform acceleration has a constant change in velocity.
5. The acceleration due to gravity is always directed towards the center of the Earth.

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Section C: Short-Answer Questions

1. Difference between uniform and non-uniform acceleration:

   • Uniform acceleration: The acceleration remains constant. Example: A freely falling object.
   • Non-uniform acceleration: The acceleration changes over time. Example: A car moving through traffic.

2. Velocity is a vector quantity because it has both magnitude and direction, whereas speed is a scalar quantity because it has only magnitude and no direction.

3. Derivation of equation of motion $v = u + at$:

   • Acceleration is defined as: $$a = \frac{v - u}{t}$$
   • Rearranging, we get: $$v = u + at$$
     

4. Retardation (negative acceleration) occurs when velocity decreases over time. Example: A car coming to a stop when brakes are applied.

5. An object moving in a circular path at constant speed has acceleration because its direction is continuously changing, leading to a change in velocity.

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Section D: Numerical Problems

1. Find acceleration

   • Given: $u = 10$ m/s, $v = 25$ m/s, $t = 5$ s
   • Using $a = \frac{v - u}{t}$
     $$a = \frac{25 - 10}{5} = \frac{15}{5} = 3 \text{ m/s²}$$
     

2. Find distance covered

   • Given: Speed $v = 18$km/h, Time $t = 10$min
   • Convert speed to m/s: $$18 \times \frac{1000}{3600} = 5 \text{ m/s}$$
     
   • Convert time to seconds: $$10 \times 60 = 600 \text{ s}$$
     
   • Distance $s = v \times t$: $$5 \times 600 = 3000 \text{ m} = 3 \text{ km}$$
     

3. Find time taken to reach the highest point

   • Given: $u = 20$ m/s, $v = 0$, $g = -9.8$ m/s²
   • Using $v = u + at$: $$0 = 20 - 9.8t$$
     $$t = \frac{20}{9.8} \approx 2.04 \text{ s}$$
     

4. Find acceleration and distance before stopping

   • Given: $u = 20$m/s, $v = 0$, $t = 10$ s
   • Acceleration: $$a = \frac{v - u}{t} = \frac{0 - 20}{10} = -2 \text{ m/s²}$$
     
   • Distance: Using $s = ut + \frac{1}{2} at^2$
     $$s = 20(10) + \frac{1}{2} (-2)(10)^2$$
     $$s = 200 - 100 = 100 \text{ m}$$
     

5. Find velocity and distance covered

   • Given: $u = 0$, $a = 4$m/s², $t=\mathrm{5<span\; style="font-family:\; verdana;"> s</span>}$
   • Final velocity: $v = u + at$
     $$v = 0 + 4(5) = 20 \text{ m/s}$$
     
   • Distance covered: Using $s = ut + \frac{1}{2} at^2$
     $$s = 0(5) + \frac{1}{2} (4)(5)^2$$
     $$\mathrm{<br>}$$