MCQ: Velocity-Time Graphs - Class 9 MCQ

• The area under the velocity-time graph represents the total change in position over time.
• This area can be positive or negative, indicating direction, hence it measures displacement.
• Displacement is the net change in position, while distance measures the total path traveled.
• Speed is the magnitude of velocity, and acceleration measures the change in velocity over time.
• Thus, the correct answer is displacement as represented by the area under the graph.

Topic in NCERT: Velocity-Time Graphs

Line in NCERT: "The area enclosed by velocity-time graph and the time axis will be equal to the magnitude of the displacement."

Velocity-Time Graph Analysis:
- The slope of the velocity-time graph gives the acceleration of the particle.
- If the velocity-time graph is a straight line, the acceleration is constant.
- The acceleration can be calculated by finding the slope of the line.
Calculating Acceleration:
- The acceleration can be calculated using the formula: acceleration = change in velocity / change in time.
- By looking at the graph, we can see that the change in velocity is 10 m/s and the change in time is 4 seconds.
Acceleration Calculation:
- acceleration = change in velocity/ time
- acceleration = 10-5 / 2 = 2.5 m/s²
Therefore, the acceleration of the particle is 2.5 m/s². Hence, the correct answer is option D: 2.5 m/s²

Option B is correct .

The maximum acceleration occurs during segment B to C as it has the steepest slope on the graph, representing the highest rate of change of velocity.

Topic in NCERT: Velocity-Time Graphs and Distance Calculation

Line in NCERT: "Since the magnitude of the velocity of the car is changing due to acceleration, the distance s travelled by the car will be given by the area ABCDE under the velocity-time graph."

In the given graph we find that the velocity is constant throughout, hence the object represented in the v - t graph is said to be in uniform motion.  Zero acceleration is also called uniform acceleration.

v = (6 - 0) m / (3 - 0) s = 2 m/s

The correct answer is D: Both (a) and (b).

• Acceleration is the rate of change of velocity. It can be positive (increasing velocity) or negative (decreasing velocity).
• Retardation is another term specifically used for negative acceleration. It describes a situation where the velocity is slowing down.

Therefore, when the velocity of a body is reducing, it has both:

• Negative acceleration: Because the change in velocity is negative.
• Retardation: Because it's the specific term for negative acceleration in the context of slowing down.

Topic in NCERT: Acceleration

Line in NCERT: "the acceleration is taken to be positive if it is in the direction of velocity and negative when it is opposite to the"

- In a velocity-time graph:
- The Y-axis represents Velocity.
- The X-axis represents Time.
- Thus, the variable plotted on the Y-axis is Velocity.

The area under the velocity-time graph gives the distance (magnitude of displacement) which has the unit: metre (m)

Topic in NCERT: VELOCITY-TIME GRAPHS

Line in NCERT: "The area under the velocity-time graph gives the distance (magnitude of displacement) moved by the car in a given interval of time."

The correct answer is C: the acceleration.

• A velocity-time graph shows how velocity changes over time.
• The slope of this graph represents the rate of change of velocity, which is acceleration.
• If the slope is positive, the object is accelerating; if negative, it's decelerating.
• Slope is calculated as the change in velocity divided by the change in time.
• Thus, a steeper slope indicates a greater acceleration.

- The area under the velocity-time graph represents displacement.
- In physics, displacement is the change in position of an object and is a vector quantity.
- The graph's area considers both magnitude and direction, reflecting total displacement.
- If velocity is constant, displacement is simply velocity multiplied by time.
- Positive and negative areas (above and below the time axis) indicate direction changes in motion.
- Therefore, the correct answer is B: displacement.