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State Board · Class 7 · General Science

Lesson 7: Motion, Force and Work

5 concepts · 40 practice questions with answers · Free to read

This lesson is also in: मराठी

Distance and displacement

From daily life

You walk from your house to a shop by the road, turn into a lane and reach it. Your friend says, "As the crow flies, it is much nearer." Both are right: one speaks about the path you walked, the other about the straight line.

Simple definition

Distance (अंतर) is the length of the actual path travelled (scalar). Displacement (विस्थापन) is the shortest straight-line distance from the start to the end, with direction (vector). SI unit of both: metre.

600 m200 mABC

In the figure : In the figure a walker goes 600 m from A to B and then 200 m back from B to C. The distance is the whole path. The displacement is the straight line from A to C.

Rule 1: Distance is the whole path — Add the lengths of all parts of the path, whatever the direction.

  • Easy : A boy walks 300 m east and then 400 m north. Distance = 300 + 400 = 700 m.
  • Medium : A girl walks 500 m forward and 150 m back. Distance = 500 + 150 = 650 m.
  • Exam-type : A dog runs 80 m, 60 m and 40 m in three turns: distance = 80 + 60 + 40 = 180 m.
500 m400 m300 mABCD

In the figure : In the figure a walker goes along the sides AB = 400 m and BC = 300 m of a rectangle. The distance is 400 + 300 = 700 m, but the displacement is the straight line AC = 500 m.

Rule 2: Displacement is the straight line — Displacement joins the start to the end and has a direction. If you return to the start, the displacement is zero.

  • Easy : 500 m forward and 150 m back: displacement = 500 − 150 = 350 m forward.
  • Medium : 300 m east then 400 m north: displacement is the straight line, 500 m (a 3-4-5 triangle).
  • Exam-type : A boy goes once round a 200 m circular ground and stops at the start: distance 200 m, displacement 0.
Remember

Distance ≥ displacement. They are equal only for motion along a straight line without turning back.

Common mistake

Writing displacement as the total path. Displacement is the straight line from start to end.

Shortcut

Memory clue: Distance = Diary of the whole path; Displacement = Direct line.

Spot the difference

PointDistanceDisplacement
MeasuresLength of pathStraight line start to end
TypeScalarVector
Can it be zero?Not if you movedYes, on returning to the start

Practice questions

Easy
  1. 1What is distance?
  2. 2What is displacement?
  3. 3Which is a vector: distance or displacement?
Medium
  1. 4Write the SI unit of distance.
  2. 5A boy walks 300 m east and 400 m north. Find the distance.
  3. 6A girl walks 500 m forward and 150 m back. Find the distance and the displacement.
Challenging
  1. 7A boy goes once round a 200 m circular ground and stops where he started. Find the distance and the displacement.
  2. 8Ravi walks 300 m east and then 400 m north. Why is his displacement 500 m and not 700 m?
Show answers (try them yourself first)
  1. 1The length of the actual path travelled.
  2. 2The shortest straight-line distance from start to end, with direction.
  3. 3Displacement
  4. 4Metre
  5. 5300 + 400 = 700 m
  6. 6Distance 650 m; displacement 350 m forward.
  7. 7Distance 200 m; displacement 0.
  8. 8Displacement is the straight line from start to end (3-4-5 triangle), not the path.

Speed and velocity

From daily life

A bus takes 2 hours to go from one town to another 120 km away. We say it runs at 60 km per hour. If someone adds "towards Nashik", we also know the direction.

Simple definition

Speed (चाल) = distance ÷ time. Velocity (वेग) = displacement ÷ time (with direction). Unit: m/s.

Rule 1: Speed — Speed = distance ÷ time. It is a scalar. If equal distances are covered in equal times, the speed does not change.

  • Easy : A cyclist covers 90 m in 30 s: speed = 90 ÷ 30 = 3 m/s.
  • Medium : A bus covers 120 km in 2 h: speed = 120 ÷ 2 = 60 km/h.
  • Exam-type : A runner goes once round a 400 m track in 80 s: speed = 400 ÷ 80 = 5 m/s, but displacement is 0, so velocity = 0.
0 s0 m1 s20 m2 s40 m3 s60 m4 s80 m

In the figure : In the figure a car is at 0 m, 20 m, 40 m, 60 m and 80 m at 0 s, 1 s, 2 s, 3 s and 4 s. Equal distances in equal times mean the speed is steady: 80 m ÷ 4 s = 20 m/s.

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Speed and velocity

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Rule 2: Velocity — Velocity = displacement ÷ time, in a given direction. Average velocity is total displacement ÷ total time. The velocity at a particular moment is the instantaneous velocity.

  • Easy : A train goes 150 km towards Pune in 3 h: velocity = 150 ÷ 3 = 50 km/h towards Pune.
  • Medium : A van covers 20 km in the first 30 min and 30 km in the next 30 min in a straight line: average velocity = 50 ÷ 1 = 50 km/h.
  • Exam-type : A truck goes 12 km in 15 min (0.25 h): velocity = 12 ÷ 0.25 = 48 km/h.
Remember

Speed has no direction; velocity has direction. Both are in m/s.

Common mistake

Using total time with only part of the distance. Use matching distance and time.

Shortcut

Memory clue: Speed = Space covered per second; Velocity = Voyage with direction: speed uses distance, velocity uses displacement.

Spot the difference

PointSpeedVelocity
FormulaDistance ÷ timeDisplacement ÷ time
TypeScalarVector
Unitm/sm/s

Practice questions

Easy
  1. 1Write the formula of speed.
  2. 2Write the formula of velocity.
  3. 3Write the SI unit of speed.
Medium
  1. 4A cyclist covers 90 m in 30 s. Find the speed.
  2. 5A train goes 150 km towards Pune in 3 h. Find its velocity.
  3. 6What is instantaneous velocity?
Challenging
  1. 7A runner goes once round a 400 m track in 80 s. Find his speed and his average velocity.
  2. 8A van covers 20 km in the first 30 min and 30 km in the next 30 min along a straight road. Find the average velocity.
Show answers (try them yourself first)
  1. 1Speed = distance ÷ time
  2. 2Velocity = displacement ÷ time
  3. 3m/s
  4. 490 ÷ 30 = 3 m/s
  5. 5150 ÷ 3 = 50 km/h towards Pune
  6. 6The velocity at a particular moment.
  7. 7Speed = 400 ÷ 80 = 5 m/s; displacement is 0, so velocity = 0.
  8. 8(20 + 30) ÷ 1 h = 50 km/h

Acceleration

From daily life

When a bus driver presses the accelerator, the bus picks up speed. When he presses the brake, it slows down. When the bus turns, its direction changes. In all these, the velocity changes.

Simple definition

Acceleration (त्वरण) = change in velocity ÷ time taken. Unit: m/s2. The interaction that causes acceleration is force.

0 s0 m1 s5 m2 s15 m3 s30 m4 s50 m

In the figure : In the figure a car is at 0 m, 5 m, 15 m, 30 m and 50 m at 0 s to 4 s. It covers more distance in each next second (5, 10, 15, 20 m), so its velocity changes: it has acceleration.

Rule 1: Acceleration formula — Acceleration = (final velocity − initial velocity) ÷ time. A toy car hitting a wall, a kicked football and a truck's accelerator all change velocity.

  • Easy : A bike's velocity rises from 2 m/s to 8 m/s in 3 s: a = (8 − 2) ÷ 3 = 2 m/s2.
  • Medium : A car goes from 10 m/s to 30 m/s in 5 s: a = (30 − 10) ÷ 5 = 4 m/s2.
  • Exam-type : A cart at 20 m/s stops in 4 s: a = (0 − 20) ÷ 4 = −5 m/s2. The minus sign means the velocity decreases.
Time (s)Velocity (m/s)021528311

In the figure : In the figure the velocity is 2, 5, 8 and 11 m/s at 0, 1, 2 and 3 s. It rises by 3 m/s every second, so the acceleration is (11 − 2) ÷ 3 = 3 m/s2.

Rule 2: Velocity can change in size or in direction — Speeding up, slowing down and turning all mean acceleration. If the velocity is steady, the acceleration is zero.

  • Easy : A car moving at a steady 20 m/s has acceleration 0.
  • Medium : A train goes from 0 to 15 m/s in 10 s: a = 15 ÷ 10 = 1.5 m/s2.
  • Exam-type : A ball's velocity increases by 4 m/s every second. In 5 s its velocity rises by 4 × 5 = 20 m/s.
Remember

Acceleration = change in velocity ÷ time. Unit: m/s2.

Common mistake

Using the final velocity instead of the change. Always subtract the initial velocity.

Shortcut

Memory clue: "A = Change in V over Time": (v − u) ÷ t.

Spot the difference

SituationVelocityAcceleration
Steady speed, straight lineConstantZero
Speeding upIncreasesPositive
Slowing downDecreasesNegative

Practice questions

Easy
  1. 1What is acceleration?
  2. 2Write the SI unit of acceleration.
  3. 3What causes acceleration?
Medium
  1. 4A bike's velocity changes from 2 m/s to 8 m/s in 3 s. Find the acceleration.
  2. 5A car goes from 10 m/s to 30 m/s in 5 s. Find the acceleration.
  3. 6What is the acceleration of a car moving at a steady velocity?
Challenging
  1. 7A train goes from rest to 15 m/s in 10 s. Find the acceleration.
  2. 8A cart moving at 20 m/s stops in 4 s. Find its acceleration and explain the sign.
Show answers (try them yourself first)
  1. 1Change in velocity per unit time.
  2. 2m/s2
  3. 3Force
  4. 4(8 − 2) ÷ 3 = 2 m/s2
  5. 5(30 − 10) ÷ 5 = 4 m/s2
  6. 6Zero
  7. 715 ÷ 10 = 1.5 m/s2
  8. 8(0 − 20) ÷ 4 = −5 m/s2; the minus sign shows that velocity decreases.

Force and Newton's first law of motion

From daily life

A marble rolling on a smooth floor goes far, but on a rough carpet it stops soon. The roughness pushes against its motion. A marble on a table stays at rest until something moves it.

Simple definition

Force (बल) is a push or pull that changes the velocity of a body. Newton's first law: a body stays at rest or keeps moving with the same velocity unless a force acts on it.

ABmotion

In the figure : In the figure a block moves to the right under the pull A. The force of friction B acts opposite to the motion. If no friction acted, a moving block would keep the same velocity.

Rule 1: Newton's first law — With no force, a stationary body stays stationary and a moving body keeps its velocity and direction. A carrom coin stops because of friction; with talcum powder it goes farther.

  • Easy : A book on a table stays at rest.
  • Medium : When a bus brakes suddenly, the passengers lean forward because their bodies tend to keep moving.
  • Exam-type : A ball rolls farther on smooth ice than on rough grass because friction is less on ice.

Rule 2: Measuring force — Force is measured by the acceleration it produces. A force that gives a 1 kg body an acceleration of 1 m/s2 is 1 newton (N). The CGS unit is the dyne.

  • Easy : The SI unit of force is the newton.
  • Medium : Pushing a cart and pulling a rope are both forces.
  • Exam-type : When no force acts, the acceleration of a body is zero.
Remember

No force means no change in velocity. Friction is the force that stops moving things.

Common mistake

Thinking a force is needed to keep a body moving at steady velocity. It is needed only to change the velocity.

Shortcut

Memory clue: "Lazy Law": a body is lazy, it keeps its state until a force acts.

Spot the difference

PointDetail
LawNo force, no change in velocity
Unit (SI)Newton (N)
Unit (CGS)Dyne
Stops moving thingsFriction

Practice questions

Easy
  1. 1What is force?
  2. 2State Newton's first law.
  3. 3What is the SI unit of force?
Medium
  1. 4What is the CGS unit of force?
  2. 5What force stops a moving carrom coin?
  3. 6Define 1 newton.
Challenging
  1. 7Why do passengers lean forward when a bus brakes suddenly?
  2. 8A ball rolls 30 m on rough grass but 80 m on smooth ice after the same push. Explain.
Show answers (try them yourself first)
  1. 1A push or pull that changes the velocity of a body.
  2. 2A body stays at rest or keeps moving with the same velocity unless a force acts on it.
  3. 3Newton (N)
  4. 4Dyne
  5. 5Friction
  6. 6The force that gives a 1 kg body an acceleration of 1 m/s2.
  7. 7Their bodies tend to keep moving with the same velocity (first law).
  8. 8Friction is less on ice, so the ball slows down less and goes farther.

Work

From daily life

Pushing a loaded cart along a road is work. Pushing a huge wall that does not move, even though you get tired, is not work in science. Work needs a force and a movement.

Simple definition

Work (कार्य) = force × displacement in the direction of the force. SI unit: joule (J); CGS unit: erg. The ability to do work is energy (ऊर्जा).

F = 15 Ns = 6 m

In the figure : In the figure a cart is pulled by a force F = 15 N through a displacement s = 6 m. Work = force × displacement = 15 × 6 = 90 J.

Rule 1: Work formula — W = F × s. 1 joule is the work done when a force of 1 N moves a body through 1 m.

  • Easy : A force of 20 N moves a box 5 m: W = 20 × 5 = 100 J.
  • Medium : A force of 50 N moves a trolley 4 m: W = 50 × 4 = 200 J.
  • Exam-type : A force of 300 N lifts a load 12 m: W = 300 × 12 = 3600 J.
F = 250 N

In the figure : In the figure a person pushes a wall with a force F = 250 N. The wall does not move, so the displacement is zero and no work is done.

Rule 2: No displacement, no work — If the body does not move, the displacement is zero, so the work is zero however large the force is.

  • Easy : Holding a heavy bag still: work = 0.
  • Medium : Pushing a rock with 400 N that does not move: W = 400 × 0 = 0 J.
  • Exam-type : If W = 90 J and F = 15 N, then s = 90 ÷ 15 = 6 m.
Remember

Work needs both force and displacement. W = F × s, in joules.

Common mistake

Saying work is done when you only feel tired. If nothing moves, work is zero.

Shortcut

Memory clue: "Work = Fs": Force × Shift; no shift, no work.

Spot the difference

PointDetail
FormulaW = F × s
SI unitJoule (J)
CGS unitErg
Zero work whenDisplacement is zero

Practice questions

Easy
  1. 1Write the formula of work.
  2. 2Write the SI unit of work.
  3. 3What is the CGS unit of work?
Medium
  1. 4What is energy?
  2. 5A force of 20 N moves a box 5 m. Find the work done.
  3. 6A force of 50 N moves a trolley 4 m. Find the work done.
Challenging
  1. 7A force of 300 N lifts a load through 12 m. Find the work done.
  2. 8Rohan pushes a wall with 250 N for 10 minutes but it does not move. What work does he do, and why?
Show answers (try them yourself first)
  1. 1W = F × s
  2. 2Joule (J)
  3. 3Erg
  4. 4The ability to do work.
  5. 520 × 5 = 100 J
  6. 650 × 4 = 200 J
  7. 7300 × 12 = 3600 J
  8. 8Zero, because the displacement is zero.

Quick revision

  • Speed = distance / time; velocity = displacement / time.
  • Acceleration = change in velocity / time.
  • Newton's first law.
  • W = F × s (joule).
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Quick revision

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