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Q1. The three equations of motion can be derived using:
The three equations of motion (v = u + at, s = ut + ½at², and v² = u² + 2as) can be derived using both graphical methods (from velocity-time graphs) and algebraic methods (from the definitions of acceleration and velocity). Both approaches give the same results.
Q2. The set of equations v = u + at, s = ut + ½at² and 2as = v² – u² are known as:
These three equations are collectively called the equations of motion. They describe the relationship between velocity, acceleration, time, and displacement for an object moving with uniform acceleration in a straight line.
Q3. The total area under a velocity-time graph for an accelerating object is the sum of a rectangle and a:
For an object moving with uniform acceleration, the velocity-time graph is a straight line. The area under this graph can be divided into a rectangle (representing distance covered due to initial velocity) and a triangle (representing additional distance covered due to acceleration).
Q4. What does the area under a velocity-time graph represent?
The area under a velocity-time graph gives the distance (or displacement) traveled by the object. This is because distance = velocity × time, and the area under the curve represents this product.
Q5. In graphical derivation, the area under a velocity-time graph gives:
In the graphical method of deriving equations of motion, the area under the velocity-time graph represents the total distance travelled by the object during the given time interval.
Q6. The equations of motion connect velocity, acceleration, time and:
The equations of motion relate the quantities: initial velocity (u), final velocity (v), acceleration (a), time (t), and distance or displacement (s). They do not involve energy, force, or mass.
Q7. What is the nature of a distance-time graph for non-uniform motion?
In non-uniform motion, the speed is not constant, so the distance covered in equal time intervals is not the same. This results in a curved distance-time graph, not a straight line.
Q8. Which of the following graphs can have any shape?
When acceleration is non-uniform, the velocity changes in an irregular manner, so the velocity-time graph can have any shape (curved, zigzag, etc.). For uniform velocity or uniform acceleration, the graphs have specific fixed shapes.
Q9. The equation v = u + at is derived from the definition of:
The equation v = u + at is derived from the definition of acceleration, which is the rate of change of velocity. Acceleration a = (v – u)/t. Rearranging gives v = u + at.
Q10. Which equation of motion describes the velocity-time relation?
The equation v = u + at gives the relationship between velocity and time. It tells us how the final velocity (v) changes with time (t) when the initial velocity (u) and acceleration (a) are known.
Q11. For an object thrown upwards and then falling down, the velocity-time graph has negative slope when it is:
When an object is thrown upwards, gravity acts downwards, causing deceleration (negative acceleration). On the way down, gravity causes acceleration downwards, which appears as a negative slope on the velocity-time graph if upward direction is taken as positive.
Q12. The slope of a velocity-time graph gives:
The slope of a velocity-time graph is calculated as change in velocity divided by change in time. This is exactly the definition of acceleration. A steeper slope means greater acceleration.
Q13. What does a negative slope on a velocity-time graph indicate?
A negative slope on a velocity-time graph means the velocity is decreasing with time. This indicates negative acceleration, also called retardation or deceleration.
Q14. What can the shape of a velocity-time graph be for non-uniformly accelerated motion?
For non-uniformly accelerated motion, the acceleration changes with time, so the velocity-time graph can have any shape depending on how the acceleration varies. It is not restricted to straight lines or specific curves.
Q15. What is the purpose of plotting graphs in the study of motion?
Graphs provide a visual and convenient way to represent motion data. They make it easier to understand relationships between quantities like distance, velocity, acceleration, and time, and allow us to derive useful information from the data.
Q16. How does the line look on a velocity-time graph for an object moving with uniform velocity?
When an object moves with uniform velocity, its velocity does not change with time. So the velocity remains constant, and the graph is a horizontal straight line parallel to the time axis.
Q17. What can you say about an object if its distance-time graph is a straight line sloping upwards?
A straight line sloping upwards on a distance-time graph means the distance is increasing at a constant rate. This indicates that the object is moving with uniform speed.
Q18. On a velocity-time graph, what is represented on the x-axis?
On a velocity-time graph, the x-axis (horizontal axis) represents time, while the y-axis (vertical axis) represents velocity. The slope of the graph gives acceleration.
Q19. For uniformly accelerated motion, the velocity-time graph is a:
For uniformly accelerated motion, the velocity changes at a constant rate. Therefore, the velocity-time graph is a straight line (not necessarily parallel to the time axis). The slope of this line gives the acceleration.
Q20. In the equation v = u + at, what does ‘u’ represent?
In the first equation of motion v = u + at, the symbol ‘u’ represents the initial velocity of the object at the start of the time interval. ‘v’ is the final velocity, ‘a’ is acceleration, and ‘t’ is time.
Q21. The slope of a distance-time graph gives the ________ of the object.
The slope of a distance-time graph gives the speed of the object. It is calculated as change in distance divided by change in time, which is the definition of speed.
Q22. When acceleration is uniform, the velocity-time graph has constant:
For uniform acceleration, the velocity changes at a constant rate. This means the slope of the velocity-time graph (which represents acceleration) is constant. The graph is a straight line with a constant slope.
Q23. The equations of motion are applicable when motion has:
The three equations of motion are specifically applicable for motion along a straight line with uniform (constant) acceleration. They cannot be directly applied when acceleration is changing or when motion is not in a straight line.
Q24. What is measured by the area under a velocity-time graph?
The area under a velocity-time graph represents the total distance (or displacement) covered by the object during the time interval. This is a fundamental concept used in graphical analysis of motion.
Q25. The area of a rectangle on a velocity-time graph represents:
On a velocity-time graph, a rectangle is formed when velocity is constant. The area of this rectangle (height × width = velocity × time) gives the distance moved by the object during that time interval at uniform velocity.
Q26. In the graphical method, the change in velocity (v − u) is represented by the line segment:
In the typical velocity-time graph, the vertical line segment AD (from the initial velocity to the final velocity) represents the change in velocity (v – u). This is used in deriving the equations of motion.
Q27. What does a straight line parallel to the time axis on a speed-time graph indicate?
A horizontal straight line parallel to the time axis on a speed-time graph means the speed is not changing with time. This indicates that the object is moving with constant speed.
Q28. Which part of the velocity-time graph represents the time interval ‘t’?
In a velocity-time graph, the horizontal distance along the time axis from O to C represents the time interval ‘t’. The vertical distance represents velocity, and the area under the graph gives distance.
Q29. For uniform acceleration, the area under velocity-time graph is a:
For uniform acceleration, the velocity-time graph is a straight line. The area under this graph forms a trapezium (if initial velocity is not zero) or a triangle (if initial velocity is zero). The trapezium area gives the distance travelled.
Q30. In the equation s = ut + ½at², ‘s’ represents:
In the second equation of motion s = ut + ½at², the symbol ‘s’ represents the distance travelled (or displacement) by the object during the time ‘t’. It is the sum of the distance due to initial velocity (ut) and the distance due to acceleration (½at²).
Q31. The nature of a straight-line velocity-time graph shows that velocity changes by:
A straight-line velocity-time graph indicates uniform acceleration. This means the velocity changes by equal amounts in equal intervals of time. The slope of the line is constant.
Q32. Which equation of motion represents the position-time relation?
The equation s = ut + ½at² represents the position-time relation because it gives the distance (s) as a function of time (t), when initial velocity (u) and acceleration (a) are known.
Q33. Drivers are advised to maintain distance between vehicles because of:
Maintaining distance between vehicles is related to all three equations of motion. The equation v² = u² + 2as helps calculate stopping distance, s = ut + ½at² gives reaction distance, and v = u + at relates to braking time. All are relevant to road safety.
Q34. On a velocity-time graph, what is represented on the y-axis?
On a velocity-time graph, the y-axis (vertical axis) represents velocity, while the x-axis (horizontal axis) represents time. The graph shows how velocity changes with time.
Q35. What type of variation does a curved distance-time graph show?
A curved distance-time graph indicates that the speed of the object is changing with time. This is a characteristic of non-uniform motion. In uniform motion, the graph is a straight line.
Q36. What does a curved line on a velocity-time graph signify?
A curved line on a velocity-time graph means the slope of the graph is changing, which indicates that the acceleration is not constant. This is called non-uniform acceleration.
Q37. The term “uniform” in uniform acceleration means:
Uniform acceleration means that the velocity of the object changes by equal amounts in equal intervals of time. The rate of change of velocity (acceleration) is constant.
Q38. If an object starts from rest, its initial velocity ‘u’ is:
“Starts from rest” means the object is not moving at the beginning of the motion. Therefore, its initial velocity u = 0 m/s. This is a common condition in many physics problems.
Q39. If the velocity of an object is decreasing with time, its velocity-time graph will slope:
If velocity is decreasing with time, the velocity-time graph has a downward slope. This indicates negative acceleration (retardation). The line goes downwards as we move from left to right.
Q40. What does a straight line sloping upwards on a velocity-time graph indicate?
A straight line sloping upwards on a velocity-time graph means the velocity is increasing at a constant rate. This indicates uniform acceleration. The slope of the line gives the magnitude of the acceleration.
Q41. When the velocity of a car is constant, the height of its velocity-time graph:
When velocity is constant, the velocity-time graph is a horizontal line. The height of this line (the velocity value) remains the same at all points in time, so it does not change with time.
Q42. What does a straight line parallel to the time axis on a distance-time graph indicate?
A straight line parallel to the time axis on a distance-time graph means the distance is not changing with time. The object is staying at the same position, which means it is at rest.
Q43. The formula for the area of a trapezium is used to derive which equation?
The area under a velocity-time graph for uniform acceleration forms a trapezium. The area of this trapezium gives the distance s. Using the trapezium area formula, we derive s = ut + ½at².
Q44. What is the shape of a distance-time graph for an object moving with uniform speed?
When an object moves with uniform speed, it covers equal distances in equal intervals of time. So the distance-time graph is a straight line inclined to the time axis.
Q45. The equation 2as = v² – u² represents the relation between:
The third equation of motion v² = u² + 2as (or 2as = v² – u²) relates the position (s) and velocity (v) of the object. It does not involve time, so it is useful when time is not known.
Q46. Equations relating velocity, acceleration, time and distance are applicable for:
The three equations of motion are specifically applicable for motion along a straight line with uniform acceleration. They cannot be directly applied to circular motion or when acceleration is changing.
Q47. If the distance-time graph is a straight line parallel to the time axis, the slope is:
A horizontal line parallel to the time axis has zero slope. This means the distance is not changing with time, indicating that the object is at rest. The slope of a distance-time graph gives speed, which is zero here.
Q48. For uniform motion, the distance-time graph is linear because distance is ________ to time.
In uniform motion, distance is directly proportional to time. This means as time increases, distance increases by the same factor. This linear relationship gives a straight-line graph passing through the origin.
Q49. The key feature of a graph representing uniform motion is that:
In uniform motion, the rate of change of distance (speed) is constant. On a distance-time graph, this shows as a constant slope. On a velocity-time graph, it shows as a horizontal line with zero slope (constant velocity).