Calculating Speed and Distance

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Questions and Answers

Explain the difference between speed and velocity, highlighting a scenario where they would have different values?

Speed is the rate at which an object is moving, while velocity is the rate at which an object is moving in a specific direction. If an object changes direction, its velocity changes, but its speed might remain constant.

Under what specific condition(s) does the magnitude of an object's average velocity equal its average speed?

When the object moves in a straight line without changing direction.

Explain what the odometer of a car measures.

The odometer measures the total distance traveled by the car.

Describe what the path of an object looks like when it is in uniform motion and justify your answer.

<p>The path is a straight line. Uniform motion implies constant velocity, meaning no change in speed or direction.</p> Signup and view all the answers

Convert 50 km/h to m/s, showing the conversion factors used.

<p>50 km/h = 50 * (1000 m / 1 km) * (1 h / 3600 s) = 13.9 m/s</p> Signup and view all the answers

Usha swims in a 90 m long pool. She covers 180 m in one minute by swimming to one end and back. What is her average speed?

<p>3 m/s</p> Signup and view all the answers

Usha swims in a 90 m long pool. She covers 180 m in one minute by swimming to one end and back. What is her average velocity?

<p>0 m/s</p> Signup and view all the answers

Explain in what kind of motion the velocity varies with time.

<p>Non-uniform motion.</p> Signup and view all the answers

Define acceleration and provide its formula.

<p>Acceleration is the rate of change of velocity per unit time. Formula: $a = (v - u) / t$</p> Signup and view all the answers

What are the sign conventions for acceleration and what do they indicate?

<p>Positive acceleration means acceleration is in the direction of velocity, while negative acceleration (deceleration) means it is opposite to the direction of velocity.</p> Signup and view all the answers

What is the SI unit of acceleration?

<p>m/s²</p> Signup and view all the answers

Describe uniform acceleration. Give an example.

<p>Uniform acceleration is when an object's velocity changes by equal amounts in equal intervals of time. Example: A freely falling body.</p> Signup and view all the answers

Give an example of non-uniform acceleration.

<p>A car traveling along a straight road increases its speed by unequal amounts in equal intervals of time.</p> Signup and view all the answers

Give an example of a motion when acceleration is in the direction of motion.

<p>A car accelerating from rest.</p> Signup and view all the answers

Give an example of a motion when acceleration is against the direction of motion.

<p>A car braking to stop.</p> Signup and view all the answers

Rahul paddles his bicycle from rest to attain a velocity of 6 m/s in 30 s. Calculate his acceleration.

<p>0.2 m/s²</p> Signup and view all the answers

Rahul, moving at 6 m/s, applies brakes and his velocity decreases to 4 m/s in 5 s. Calculate his acceleration.

<p>-0.4 m/s²</p> Signup and view all the answers

Define uniform acceleration in your own words.

<p>Uniform acceleration is when the velocity of an object changes at a constant rate.</p> Signup and view all the answers

A bus decreases its speed from 80 km/h to 60 km/h in 5 seconds. Calculate the acceleration of the bus in m/s².

<p>-1.11 m/s²</p> Signup and view all the answers

A train accelerates uniformly from rest and attains a speed of 40 km/h in 10 minutes. Find its acceleration in m/s².

<p>0.0185 m/s²</p> Signup and view all the answers

Flashcards

Acceleration

The rate of change of velocity of an object.

Uniform Acceleration

Motion with constant acceleration.

Non-uniform Acceleration

Motion where acceleration is not constant.

Distance

The total path length covered by an object.

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Displacement

The shortest distance between initial and final positions.

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Average Speed

Total distance traveled divided by total time taken.

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Average Velocity

Change in position (displacement) divided by total time taken.

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Odometer

The odometer measures the distance traveled by a vehicle.

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Speed

Speed is the rate at which an object is moving.

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Velocity

Velocity is the rate at which an object is moving in a specific direction.

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Study Notes

  • When it is cloudy, thunder and lightning often occur together, but sound takes time to reach you after seeing lightning.
  • This is due to the speed of sound being slower than the speed of light

Calculating Distance of Lightning

  • Using a digital watch or stopwatch, measure the time interval between seeing lightning and hearing thunder
  • Calculate the distance to the nearest point of lightning using the speed of sound in air (346 m/s).

Average Speed Calculation (Car Example)

  • A car's odometer reads 2000 km at the start of a trip and 2400 km at the end
  • The trip took 8 hours
  • Distance covered: 2400 km - 2000 km = 400 km
  • Average speed = Total distance / Time elapsed = 400 km / 8 h = 50 km/h
  • Converting km/h to m/s: 50 km/h = 50 x (1000 m / 1 km) x (1 h / 3600 s) = 13.9 m/s

Average Speed and Velocity (Usha's Swimming Example)

  • Usha swims in a 90 m long pool, covering 180 m in one minute by swimming to one end and back
  • Total distance covered = 180 m
  • Displacement = 0 m (since she returns to the starting point)
  • Average speed = Total distance / Total time = 180 m / 1 min = 3 m/s
  • Average velocity = Displacement / Total time = 0 m / 60 s = 0 m/s

Rate of Change of Velocity

  • In uniform motion along a straight line, velocity remains constant, resulting in zero change in velocity over any time interval
  • In non-uniform motion, velocity varies with time, having different values at different instants and points along the path, resulting in a non-zero change in velocity.

Acceleration

  • Acceleration quantifies how velocity changes per unit time
  • Formula: acceleration = change in velocity / time taken
  • If an object's velocity changes from an initial value (u) to a final value (v) over a time (t), then acceleration (a) = (v - u) / t

Accelerated Motion

  • Accelerated motion occurs when an object's velocity changes over time
  • Acceleration is positive if in the direction of velocity and negative if opposite to it
  • The SI unit of acceleration is m/s²

Uniform vs Non-Uniform Acceleration

  • If an object travels in a straight line and its velocity increases or decreases by equal amounts in equal time intervals, its acceleration is uniform
  • Example: A freely falling body experiences uniform acceleration
  • If an object's velocity changes at a non-uniform rate, its acceleration is non-uniform
  • Example: A car increasing speed by unequal amounts in equal time intervals

Acceleration Calculation (Bicycle Example)

  • Rahul accelerates his bicycle from rest to 6 m/s in 30 s, then brakes to 4 m/s in 5 s
  • Case 1: u = 0 m/s, v = 6 m/s, t = 30 s; a = (6 - 0) / 30 = 0.2 m/s²
  • Case 2: u = 6 m/s, v = 4 m/s, t = 5 s; a = (4 - 6) / 5 = -0.4 m/s²

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