Q1. Analyze the motion of a projectile as shown in the diagram. What are the key features of its velocity components at different points along its path?

Background

Topic: Projectile Motion

This question tests your understanding of two-dimensional motion, specifically how the horizontal and vertical components of velocity change for a projectile under gravity.

Key Terms and Formulas:

• Projectile motion: The motion of an object thrown or projected into the air, subject only to acceleration due to gravity.

• Horizontal velocity (): (remains constant)

• Vertical velocity (): (changes due to gravity)

• At the peak:

• Range ():

• Maximum height ():

Step-by-Step Guidance

1. Identify the initial velocity components: Use and .

2. Recall that the horizontal velocity remains constant throughout the flight (no horizontal acceleration).

3. The vertical velocity decreases as the projectile rises, becomes zero at the peak, and increases in magnitude (but negative) as it falls back down.

4. At the peak of the trajectory, the vertical component of velocity is zero, but the horizontal component is unchanged.

5. Think about how the velocity vectors at different points (start, peak, end) relate to the initial components and the effect of gravity.

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Q2. The graphs below show velocity versus time for two different motions. Describe the acceleration for each case.

Background

Topic: Kinematics – Velocity-Time Graphs

This question tests your ability to interpret velocity-time graphs and relate them to acceleration.

Key Terms and Formulas:

• Acceleration (): The rate of change of velocity with respect to time, .

• On a velocity-time graph, the slope at any point gives the acceleration.

Step-by-Step Guidance

1. For the left graph: Notice the velocity changes abruptly from +1 to -1 m/s at s, and back to 0 at s.

2. For the right graph: The velocity increases smoothly from 0 to +1 m/s over 2 seconds.

3. Think about what kind of acceleration (constant, zero, or changing) would produce each graph.

4. Consider the slope of each segment: a steep, sudden change means a large (possibly infinite) acceleration; a curved line means changing acceleration.

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Q3. The graph below shows velocity versus time for an object. Describe the motion and determine when the object is at rest.

Background

Topic: Interpreting Velocity-Time Graphs

This question tests your ability to read a velocity-time graph and understand when the object changes direction or is at rest.

Key Terms and Formulas:

• Velocity (): The rate of change of position with time.

• At rest:

• Positive velocity: moving in the positive direction; negative velocity: moving in the negative direction.

Step-by-Step Guidance

1. Identify the points where the velocity crosses the time axis (). These are the moments when the object is at rest or changes direction.

2. Note the intervals where velocity is positive (object moves forward) and where it is negative (object moves backward).

3. Look for flat segments (constant velocity) and sloped segments (changing velocity, i.e., acceleration).

4. Mark the times at which to answer when the object is at rest.

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