Answer :
When an object moves with uniform positive acceleration, its motion follows certain principles of physics regarding acceleration and velocity. Let's analyze the options carefully:
1. Understanding Uniform Positive Acceleration:
- Uniform acceleration means the acceleration is constant over time.
- Positive acceleration implies that the velocity of the object is increasing over time.
2. Velocity-Time Graph Characteristics:
- When the object is accelerating uniformly, the change in velocity over time is linear.
- This means the velocity-time graph will be a straight line since the velocity increases at a constant rate.
3. Inclination of the Line:
- Parallel to the Time Axis: If the velocity-time graph were a straight line parallel to the time axis (Option a), it would imply that the velocity is constant, indicating zero acceleration. This does not match our condition of positive acceleration.
- Inclined at an Obtuse Angle: A straight line inclined at an obtuse angle to the time axis (Option b) would imply that the increase in velocity is in the negative direction over time, indicating negative acceleration (deceleration), which contradicts the positive acceleration condition.
- Inclined at an Acute Angle: A straight line inclined at an acute angle to the time axis (Option c) correctly indicates that the velocity is increasing over time and the object is accelerating positively at a uniform rate.
Given this analysis, the correct description of the velocity-time graph for an object with uniform positive acceleration is a straight line inclined at an acute angle to the time axis.
Therefore, the answer is:
(c) A straight line inclined at an acute angle to the time axis.
1. Understanding Uniform Positive Acceleration:
- Uniform acceleration means the acceleration is constant over time.
- Positive acceleration implies that the velocity of the object is increasing over time.
2. Velocity-Time Graph Characteristics:
- When the object is accelerating uniformly, the change in velocity over time is linear.
- This means the velocity-time graph will be a straight line since the velocity increases at a constant rate.
3. Inclination of the Line:
- Parallel to the Time Axis: If the velocity-time graph were a straight line parallel to the time axis (Option a), it would imply that the velocity is constant, indicating zero acceleration. This does not match our condition of positive acceleration.
- Inclined at an Obtuse Angle: A straight line inclined at an obtuse angle to the time axis (Option b) would imply that the increase in velocity is in the negative direction over time, indicating negative acceleration (deceleration), which contradicts the positive acceleration condition.
- Inclined at an Acute Angle: A straight line inclined at an acute angle to the time axis (Option c) correctly indicates that the velocity is increasing over time and the object is accelerating positively at a uniform rate.
Given this analysis, the correct description of the velocity-time graph for an object with uniform positive acceleration is a straight line inclined at an acute angle to the time axis.
Therefore, the answer is:
(c) A straight line inclined at an acute angle to the time axis.
