Physics: Distance and Velocity-Time Graphs

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Questions and Answers

What does a straight line represent on a distance-time graph?

  • Constant speed of the object (correct)
  • Variable speed of the object
  • Deceleration of the object
  • Acceleration of the object

How is speed determined from a distance-time graph?

  • By calculating the slope of the graph (correct)
  • By measuring the area under the graph
  • By analyzing the curvature of the graph
  • By counting the number of data points

What does a horizontal line indicate on a distance-time graph?

  • The object is stationary (correct)
  • The object is accelerating
  • The object is moving at a constant speed
  • The object is moving in reverse

In a distance-time graph, what does the slope represent?

<p>Speed of the object (A)</p> Signup and view all the answers

What characteristic describes a distance-time graph of an object moving at varying speeds?

<p>It has curves and angles (A)</p> Signup and view all the answers

What is the relationship between distance and displacement in a distance-time graph?

<p>Distance is usually equivalent to displacement (A)</p> Signup and view all the answers

What can be inferred about an object if the distance-time graph is steep?

<p>The object is moving at a higher speed (B)</p> Signup and view all the answers

What does the term 'scalar quantity' refer to in the context of distance?

<p>A quantity with only magnitude (A)</p> Signup and view all the answers

What is the total distance traveled by the skier during the first three minutes?

<p>420 m (D)</p> Signup and view all the answers

What does the vertical axis of a velocity-time graph represent?

<p>Velocity of the object (D)</p> Signup and view all the answers

If an object's velocity is constant, how is the line represented on a velocity-time graph?

<p>Horizontal (C)</p> Signup and view all the answers

What does the slope of a velocity-time graph represent?

<p>Acceleration (D)</p> Signup and view all the answers

In terms of the velocity-time graph, what does a straight, sloped line indicate?

<p>Constant acceleration (D)</p> Signup and view all the answers

What signifies that an object is slowing down on a velocity-time graph?

<p>A downward sloping line (D)</p> Signup and view all the answers

What does the area under the velocity-time graph indicate?

<p>Distance traveled (C)</p> Signup and view all the answers

If the slope of a velocity-time graph is calculated using the formula (y2-y1)/(x2-x1), what does y represent?

<p>Velocity (B)</p> Signup and view all the answers

What is the total area represented in a velocity-time graph if it includes a rectangle of area 300 m, a triangle of area 200 m, another rectangle of area 300 m, and two triangles of area 450 m and 300 m respectively?

<p>1550 m (C)</p> Signup and view all the answers

How is the initial velocity of an object calculated using a velocity-time graph if it travels a distance of 10 m in 10 s under constant acceleration?

<p>2 m/s (B)</p> Signup and view all the answers

What does a velocity-time graph indicate if it contains an area above the horizontal axis?

<p>Distance traveled in a positive direction (B)</p> Signup and view all the answers

Which formula is correctly used to calculate the area of a triangle on a velocity-time graph?

<p>$Area = ½ bh$ (B)</p> Signup and view all the answers

What is the significance of constant acceleration in relation to the velocity of an object?

<p>Velocity increases by the same amount each second (A)</p> Signup and view all the answers

To find the area under a velocity-time graph representing a rectangle, which of the following calculations is performed?

<p>$Area = b × h$ (D)</p> Signup and view all the answers

What would indicate a negative distance on a velocity-time graph?

<p>Area below the horizontal axis (A)</p> Signup and view all the answers

In a velocity-time graph, if the area is calculated as $Area = ½ (10)(60)$, what does this calculation depict?

<p>Area of a triangle (A)</p> Signup and view all the answers

What is the formula used to calculate final velocity as a function of time?

<p>v = u + at (C)</p> Signup and view all the answers

Which equation can be used to find displacement if the initial velocity, time, and acceleration are known?

<p>s = ut + ½at² (A)</p> Signup and view all the answers

In the equation v = u + at, what does each variable represent?

<p>v = final velocity, u = initial velocity, a = acceleration (D)</p> Signup and view all the answers

Which of the following statements is correct regarding constant acceleration?

<p>The displacement can be calculated using uniform acceleration equations. (B)</p> Signup and view all the answers

What is the relationship between the initial velocity, final velocity, and displacement according to the derived equation?

<p>v² = u² + 2as (D)</p> Signup and view all the answers

What is the final velocity of an object that has a constant acceleration of 5 m/s² over a distance of 40 m, starting from rest?

<p>20 m/s (D)</p> Signup and view all the answers

If an object is dropped from rest, how much does its velocity increase after falling for 3 seconds under gravity?

<p>20 m/s (C)</p> Signup and view all the answers

How far does an object fall in 30 seconds during a typical skydive where the acceleration due to gravity is 9.8 m/s²?

<p>4410 m (B)</p> Signup and view all the answers

What would be the distance traveled by an object moving with a constant velocity of 5 m/s over a time span of 6 seconds?

<p>30 m (B)</p> Signup and view all the answers

At what relative position on Earth would the acceleration due to gravity be expected to be highest?

<p>At the poles (A)</p> Signup and view all the answers

Which of the following correctly describes the motion of an object falling freely in a vacuum?

<p>It experiences constant acceleration. (C)</p> Signup and view all the answers

What effect does air resistance have on an object falling freely compared to one falling in a vacuum?

<p>It decreases the rate of acceleration. (A)</p> Signup and view all the answers

If the acceleration due to gravity is 9.81 m/s², what is the approximate velocity of an object after 4 seconds of free fall?

<p>39.24 m/s (B)</p> Signup and view all the answers

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Study Notes

Distance - Time Graphs

  • A distance-time graph shows the distance travelled by an object plotted against time.
  • A straight line represents constant speed.
  • The slope of the line represents the speed of the object.
  • For a stationary object, the line will be horizontal.
  • For an object at a steady speed, the line will be straight and sloping.
  • The steeper the slope, the faster the object is travelling.
  • When distance-time graphs are used to track objects moving in a straight line, the distance is equivalent to displacement.

Velocity - Time Graphs

  • A velocity-time graph shows the velocity of an object plotted against time.
  • The slope of the line represents the acceleration of the object.
  • A horizontal line represents constant velocity.
  • A straight line represents a constant acceleration.
  • The steeper the slope, the greater the acceleration.
  • The area under the graph represents the distance travelled.

Constant Acceleration

  • Acceleration is the rate of change of velocity with respect to time.
  • If the object is gaining velocity by the same amount each second, it has a constant acceleration.

Equation of Motion

  • Equations of motion describe the motion of an object moving in a straight line with constant acceleration.
  • The equations are:
    • Velocity as a function of time: v = u + at
    • Displacement as a function of time: s = ut + ½at2
    • Velocity as a function of displacement: v2 = u2 + 2as
  • Where:
    • v = final velocity
    • u = initial velocity
    • a = acceleration
    • t = time
    • s = distance

Acceleration due to Gravity

  • All objects near the earth's surface fall downwards with the same acceleration due to the force of gravity, called acceleration due to gravity (g)
  • g is approximately 10 m/s², meaning an object gains velocity by 10 m/s every second it falls.
  • The value of g varies slightly across the earth's surface, but the average value is 9.81 m/s².

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