Draw speed-time graphs for zero acceleration, uniform acceleration, and uniform deceleration. Also, show that the area under a speed-time graph represents the distance covered by the body.

Let’s first describe and draw the speed-time graphs for the three different types of motion: zero acceleration, uniform acceleration, and uniform deceleration.

1. Zero Acceleration (Constant Speed):

In this case, the speed of the object remains constant over time. Since acceleration is zero, the graph will be a horizontal line.

  • Graph: A straight horizontal line at a constant speed.
  • Description: No change in speed, so the velocity stays the same at all times.

Area under the graph: The area under the line represents the distance covered. Since the speed is constant, the area under the graph is a rectangle, calculated as:

Distance=Speed×Time

2. Uniform Acceleration (Constant Acceleration):

When an object accelerates uniformly, its speed increases at a constant rate. The graph will be a straight line with a positive slope.

  • Graph: A straight line that starts from the origin (if the object starts from rest) and increases linearly.
  • Description: The object’s speed increases constantly as time progresses.

Area under the graph: The area under the line is a triangle. The distance covered is given by the area of the triangle, which is:

Distance=1/2×Base (Time)×Height (Speed)

This formula is derived from the basic area of a triangle.

3. Uniform Deceleration (Constant Negative Acceleration):

In this case, the object’s speed decreases at a constant rate. The graph will be a straight line with a negative slope, indicating a reduction in speed.

  • Graph: A straight line sloping downward, starting from the initial speed and decreasing to zero (if the object comes to rest).
  • Description: The object’s speed decreases steadily as time passes.

Area under the graph: The area under the line is a triangle. The distance covered is:

Distance=1/2×Base (Time)×Height (Speed)

This is similar to the uniform acceleration case but with a negative slope.

Key Concept: Area Under the Speed-Time Graph Represents Distance

  • In all these graphs, the area under the graph represents the distance covered by the object.
    • For zero acceleration, the area is simply a rectangle (speed × time).
    • For uniform acceleration and deceleration, the area is a triangle, representing the distance traveled as the speed increases or decreases.

The general relationship between the area under the graph and the distance covered can be summarized as:

Distance=Area under the speed-time graph\text{Distance} = \text{Area under the speed-time graph}

This is why speed-time graphs are valuable in analyzing motion, as they provide a visual way to calculate the distance traveled over time.“

Related Questions:

  1. Differentiate between rest and motion. With the help of an example, show that rest and motion are relative to an observer.
  2. What are different types of motion? Define each type of motion with examples from daily life.
  3. What are scalars and vectors? Give examples. How are vectors represented symbolically and graphically?
  4. Define the term position. Differentiate between distance and displacement.
  5. Differentiate between speed and velocity. Also, define average speed, uniform and variable speeds, average velocity, uniform and variable velocities.
  6. What are freely falling bodies? What is gravitational acceleration? Write down sign conventions for gravitational acceleration. Write three equations of motion of a freely falling body.
  7. Draw distance-time graphs for rest, uniform speed, increasing speed, and decreasing speed.
  8. NUMERICAL RESPONSE QUESTIONS
  9. In a park, children are enjoying a ride on a Ferris wheel as shown. What kind of motion does the big wheel have, and what kind of motion do the riders have?
  10. A boy moves for some time, give two situations in which his displacement is zero but the distance covered is not zero.
  11. A stone tied to a string is whirling in a circle. What is the direction of its velocity at any instant?
  12. Is it possible to accelerate an object without speeding it up or slowing it down?
  13. Can a car moving towards the right have the direction of acceleration towards the left?
  14. With the help of daily life examples, describe the situations in which: a. Acceleration is in the direction of motion. b. Acceleration is against the direction of motion. c. Acceleration is zero and the body is in motion.
  15. Examine the distance-time graph of a motorcyclist (as shown). What does this graph tell us about the speed of the motorcyclist? Also, plot its velocity-time graph.
  16. Which controls in the car can produce acceleration or deceleration in it?
  17. If two stones of 10 kg and 1 kg are dropped from a 1 km high tower, which will hit the ground with greater velocity? Which will hit the ground first? (Neglect air resistance)
  18. A 100 g ball is just released (from rest) and another is thrown downward with a velocity of 10 m/s. Which will have greater acceleration? (Neglect air resistance)
  19. Physical Quantities and Measurement
  20. Kinematics-mcq