Year 10 Physics: Describing Motion Along A Line (Speed, Velocity, Acceleration)

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Detailed Explanation of Motion Along a Line 🚗

When studying physics in Year 10, understanding motion along a line is a key topic. It includes learning about speed, velocity, and acceleration—important concepts that describe how objects move. This section explains these terms, their formulas, units, and the differences between scalar and vector quantities. It also shows how to interpret distance-time and velocity-time graphs, which help us see motion visually.

Speed, Velocity, and Acceleration: Definitions and Formulas ⚡

• Speed is a scalar quantity that tells us how fast an object is moving regardless of direction.
  Formula:
  $$\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$$
  Units: metres per second (m/s) or kilometres per hour (km/h)
  Example: A car travels 100 metres in 5 seconds. Its speed = $\frac{\mathrm{100\; m}}{\mathrm{5\; s}}=\; 20\; m/s$.
• Velocity is a vector quantity—it has both size (magnitude) and direction. Velocity indicates speed in a certain direction.
  Formula:
  $$\mathrm{Velocity}=\frac{\mathrm{Displacement}}{\mathrm{Time}}$$
  Units: metres per second (m/s)
  Example: If the same car travels 100 metres east in 5 seconds, its velocity = $\frac{\mathrm{100\; m\; east}}{\mathrm{5\; s}}=\; 20\; m/s\; east$.
• Acceleration is the rate of change of velocity over time. It shows how quickly velocity changes, including changes in speed or direction.
  Formula:
  $$\mathrm{Acceleration}=\frac{\mathrm{Change\; in\; Velocity}}{\mathrm{Time}}$$
  Units: metres per second squared (m/s²)
  Example: If a car’s velocity increases from 0 m/s to 20 m/s in 4 seconds, acceleration =
  $\frac{\mathrm{20\; m/s\; –\; 0\; m/s}}{\mathrm{4\; s}}=\; 5\; m/s²$.

Scalar vs Vector Quantities ➕➖

• Scalar quantities have only magnitude (size). They do not include direction. Examples: speed, distance, time.
• Vector quantities include both magnitude and direction. Examples: velocity, displacement, acceleration.

Understanding the difference is essential because it affects calculations and how we interpret motion. For instance, returning to the start means displacement is zero, but distance travelled is not.

Interpreting Distance-Time and Velocity-Time Graphs 📈

• Distance-Time Graphs:
  – The slope represents speed.
  – A straight, sloping upwards line means constant speed.
  – A flat line means the object is stationary (not moving).
  – A steeper slope means a faster speed.
  – Curves show changing speeds (acceleration or deceleration).
• Velocity-Time Graphs:
  – The slope represents acceleration.
  – A flat line represents constant velocity (no acceleration).
  – A sloping line indicates acceleration (if slope is positive) or deceleration (if slope is negative).
  – The area under the graph gives displacement.

By analysing these graphs, we can better understand the motion described by speed, velocity, and acceleration. They help us visualise how an object moves along a line over time.

10 Examination-Style 1-Mark Questions with 1-Word Answers on Motion Along a Line 📝

1. What is the term for the distance travelled per unit time?
   Answer: Speed
2. What do we call velocity that includes direction?
   Answer: Velocity
3. Which quantity is a vector: speed or velocity?
   Answer: Velocity
4. What is the change in velocity divided by time called?
   Answer: Acceleration
5. What kind of acceleration occurs if an object slows down?
   Answer: Deceleration
6. What is the term for motion in a straight line?
   Answer: Linear
7. Which measure can be zero even if speed is not zero?
   Answer: Velocity
8. What does a positive acceleration indicate about the speed?
   Answer: Increasing
9. What is the SI unit for speed and velocity?
   Answer: Metres
10. What describes how fast an object changes its position?
    Answer: Speed

10 Examination-Style 2-Mark Questions with 1-Sentence Answers on Motion Along a Line 💡

1. Define speed and state its SI unit.
   Answer: Speed is the distance travelled per unit time, and its SI unit is metres per second (m/s).
2. A car travels 120 metres in 15 seconds. Calculate its average speed.
   Answer: The average speed is 120 ÷ 15 = 8 m/s.
3. Explain the difference between speed and velocity.
   Answer: Speed is scalar and only has magnitude, while velocity is a vector and includes both magnitude and direction.
4. A cyclist moves east at 5 m/s and then moves west at 3 m/s. What is the cyclist’s change in velocity?
   Answer: The change in velocity is 5 m/s east to 3 m/s west, which is 8 m/s in the opposite direction.
5. Calculate the acceleration of a car that increases its velocity from 10 m/s to 20 m/s in 5 seconds.
   Answer: Acceleration = (20 – 10) ÷ 5 = 2 m/s².
6. What does negative acceleration mean in terms of motion along a line?
   Answer: Negative acceleration means the object is slowing down or decelerating along the line.
7. A train moves with a constant velocity of 15 m/s for 30 seconds. What distance does it cover?
   Answer: Distance covered = speed × time = 15 × 30 = 450 metres.
8. Describe what is shown by a velocity–time graph that is a straight, horizontal line.
   Answer: It shows the object is moving at a constant velocity with zero acceleration.
9. An object accelerates uniformly from rest to 12 m/s in 6 seconds. What is its acceleration?
   Answer: Acceleration = 12 ÷ 6 = 2 m/s².
10. Why can an object have zero speed but still have a changing velocity?
    Answer: Because the object may be changing direction while momentarily stationary, causing the velocity to change despite zero speed.

10 Examination-Style 4-Mark Questions with 6-Sentence Answers on Motion Along a Line ✍️

Question 1

Explain what is meant by acceleration in motion along a line and describe how it affects the velocity of an object.

Answer:
Acceleration is the rate at which an object’s velocity changes over time. If an object is accelerating, its velocity is either increasing or decreasing. For example, a car speeding up on a straight road has positive acceleration. If the car slows down, it has negative acceleration (deceleration). Acceleration can change both the speed and the direction of motion if the object moves in a straight line. This means that even if the speed stays the same but direction changes, acceleration is present.

Question 2

A car moves along a straight road and its velocity-time graph is a straight line sloping upwards. What does this tell you about the car’s motion?

Answer:
A straight line sloping upwards on a velocity-time graph shows that the velocity of the car is increasing steadily over time. This means the car has a constant positive acceleration. The slope of this line represents the acceleration value. Since the velocity increases, the car is speeding up. If the line started from zero velocity, this means it began at rest and gained speed. This type of motion is typical for a car pulling away from a stationary position.

Question 3

Describe what happens to the velocity of an object when it experiences constant negative acceleration while moving in a straight line.

Answer:
Constant negative acceleration means the object is slowing down at a steady rate. The velocity decreases over time until it may reach zero if the object stops. If the object continues to decelerate past zero velocity, it will start moving backward in the opposite direction. This is sometimes called deceleration or retardation. Negative acceleration opposes the object’s motion if it initially moves forwards. For example, a bike braking to stop experiences constant negative acceleration.

Question 4

Explain with an example how speed and velocity are different when describing motion along a line.

Answer:
Speed is a scalar quantity that only tells us how fast an object is moving, without any direction. Velocity is a vector quantity that includes both speed and direction. For example, a car traveling at 30 m/s north has a velocity of 30 m/s north. If the car turns around and goes south at the same speed, its velocity changes because direction changed. The speed remains 30 m/s but the velocity becomes 30 m/s south. This difference is important because velocity tells us about motion direction as well as magnitude.

Question 5

A runner starts from rest and accelerates uniformly for 10 seconds to reach a velocity of 8 m/s. Calculate the runner’s acceleration.

Answer:
Acceleration is the change in velocity divided by the time taken. The runner starts from rest, so the initial velocity u = 0 m/s. The final velocity v = 8 m/s and the time t = 10 seconds. Using the formula a = (v – u) / t, acceleration a = (8 – 0) / 10 = 0.8 m/s². This means the runner’s velocity increases by 0.8 m/s every second. Uniform acceleration means this rate stays the same during the whole 10 seconds.

Question 6

Interpret a distance-time graph where the curve is getting steeper as time increases.

Answer:
When a distance-time graph curve gets steeper, it means the distance is increasing more quickly as time passes. This indicates the object is speeding up. The steeper the curve, the greater the speed at that instant. The curve getting steeper shows the object is accelerating in a positive direction. If the curve was a straight line, speed would be constant. So, a curve that becomes steeper shows increasing speed or positive acceleration.

Question 7

Describe what happens to an object’s acceleration if the velocity-time graph is a horizontal line above zero.

Answer:
A horizontal line on a velocity-time graph shows that velocity is constant over time. Since acceleration is the rate of change of velocity, no change means acceleration is zero. The object therefore moves at a constant velocity. It neither speeds up nor slows down. This situation occurs when forces on the object are balanced. For example, a car cruising at a constant speed along a straight road has zero acceleration.

Question 8

Explain the motion of a ball thrown straight up in terms of velocity and acceleration.

Answer:
When a ball is thrown straight up, it moves upwards, slows down, stops momentarily at the highest point, and then falls back down. The velocity decreases while going up because acceleration due to gravity acts downward. At the highest point, velocity is zero but acceleration is still downwards. As the ball falls, velocity increases downward due to the constant acceleration from gravity. This acceleration remains constant at about 9.8 m/s² downwards throughout the motion. So, velocity changes direction but acceleration stays the same.

Question 9

If an object starts with a velocity of 5 m/s and accelerates at 2 m/s² for 4 seconds, what is its final velocity?

Answer:
To find the final velocity v, use the formula v = u + at, where u = 5 m/s, a = 2 m/s², and t = 4 s.
Calculate: v = 5 + (2 × 4) = 5 + 8 = 13 m/s.
The velocity has increased because the object accelerated positively. After 4 seconds, the object moves much faster than at the start. This shows how acceleration increases velocity over time. The motion is in a straight line with constant acceleration.

Question 10

What does it mean if the velocity-time graph of an object crosses the time axis from positive to negative velocity?

Answer:
When a velocity-time graph crosses the time axis, velocity changes from positive to negative or vice versa. This means the object changes direction along the line. Positive velocity indicates motion in one direction, and negative velocity means motion in the opposite direction. Crossing the axis means the object momentarily stopped (velocity zero) before reversing. For example, a car moving forward could stop and then move backwards. This is common in motion along a single straight line with changing direction.

10 Examination-Style 6-Mark Questions with 10-Sentence Answers on Describing Motion Along a Line (Speed, Velocity, Acceleration) 🚦

1. Explain in detail the difference between speed and velocity, and give an example of a situation where they are different.
   Your answer should describe speed as a scalar quantity and velocity as a vector quantity including direction. Use a real-life example such as a car moving around a circular track.
2. A cyclist travels 30 km north in 2 hours and then 40 km south in 1 hour. Calculate the average speed and average velocity for the whole journey, showing your working clearly.
   Include explanations of total distance, displacement, time, and how these relate to speed and velocity.
3. Describe with examples how acceleration can be positive, negative, or zero, including what this means for the motion along a straight line.
   Explain the meanings of speeding up, slowing down, and constant velocity and relate these to acceleration signs.
4. A car moves along a straight road with velocity-time graph showing a straight line sloping down from +20 m/s to 0 m/s in 5 seconds. Describe what the graph tells you about the motion of the car and calculate its acceleration.
   Explain how to interpret velocity-time graphs for acceleration and the significance of the slope.
5. Explain how to calculate the distance travelled from a velocity-time graph during acceleration, and why this calculation is important in real-life situations.
   Include the concept of area under the graph and practical uses such as vehicle safety testing.
6. A person runs back and forth along a straight 100-metre track, finishing their run at the starting point in 50 seconds. Calculate their average velocity and average speed, and explain why these are different.
   Discuss displacement versus total distance in your explanation.
7. Describe a real-life scenario involving a vehicle accelerating from rest to a certain velocity and then decelerating to rest. Explain how speed, velocity, and acceleration change during each phase.
   Use detailed descriptions of speed and velocity changes and how acceleration can be positive or negative.
8. Explain why an object moving at constant speed around a circular track has changing velocity and acceleration.
   Describe how direction change affects velocity and acceleration despite constant speed.
9. A person drops a ball from a height and it accelerates as it falls. Explain the concepts of acceleration due to gravity, velocity changes, and how air resistance might affect the motion.
   Incorporate speed, velocity, and acceleration with real physical effects.
10. A velocity-time graph shows a vehicle starting from rest, accelerating uniformly for 4 seconds, travelling at constant velocity for 6 seconds, then decelerating uniformly to rest in 3 seconds. Sketch and describe the key features of the graph, including calculations for acceleration and distance travelled.
    Explain each section carefully and how to find acceleration and distance from the graph.

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