Velocity-Time Graphs

The slope of a velocity-time graph represents (a)  

• Speed
• Distance
• Acceleration
• Time

Answer explanation

The slope of a velocity-time graph represents acceleration, as it indicates the rate of change of velocity over time. A steeper slope means greater acceleration.

A boat going north is accelerating. If its velocity is measured every second and plotted on a velocity-time graph, which type of motion is represented by a positive slope?

• Speeding up

• Slowing down

• Constant velocity

• Stopping

Answer explanation

A positive slope on a velocity-time graph indicates that the velocity is increasing over time. Therefore, the boat is speeding up as it accelerates northward.

What does a flat line on a velocity-time graph indicate?

• The object is accelerating

• The object is moving at a constant velocity

• The object is slowing down

• The object is at rest

Answer explanation

A flat line on a velocity-time graph indicates that the velocity is constant over time. This means the object is moving at a constant velocity, not accelerating, slowing down, or at rest.

How would a car's velocity-time graph look if it’s slowing down at a constant rate?

• Upward sloping line

• Flat line

• Downward sloping line

• No line

Answer explanation

A car slowing down at a constant rate will show a downward sloping line on a velocity-time graph. This indicates that the velocity is decreasing over time, reflecting the constant deceleration.

Match the following scenarios with the type of acceleration they represent.

• A car’s velocity changes from 15 m/s [E] to 25 m/s [E]

• Positive acceleration

• A car travels at a steady speed of 25 m/s [E]

• No acceleration

• A car’s velocity remains at 15 m/s [E]

• Constant velocity

• A car’s velocity changes from 25 m/s [E] to 15 m/s [E]

• Negative acceleration

Answer explanation

The car's velocity increases from 15 m/s to 25 m/s in the same direction (East). This increase in speed indicates that the car is experiencing positive acceleration.

A car goes from 15 m/s [W] to 5 m/s [W]. Is the acceleration positive or negative?

• Positive acceleration

• Negative acceleration

Answer explanation

The car slows down from 15 m/s to 5 m/s, indicating a decrease in velocity. Since acceleration is defined as the change in velocity over time, this results in negative acceleration.

What is the acceleration of a car that goes from 22 m/s [N] to 0 m/s in 3.5 seconds?

• 3.5 m/s² [N]

• 6.3 m/s² [N]

• 2.3 m/s² [N]

• 9.8 m/s² [N]

Answer explanation

To find acceleration, use the formula a = (final velocity - initial velocity) / time. Here, a = (0 m/s - 22 m/s) / 3.5 s = -6.3 m/s². The negative sign indicates deceleration, so the magnitude is 6.3 m/s² [N].

If a car changes its velocity from 15 m/s [E] to 5 m/s [E], the direction of the acceleration is (a)  

• Positive
• Negative

Answer explanation

The car's velocity decreases from 15 m/s to 5 m/s, indicating a reduction in speed. This means the acceleration is in the opposite direction of the velocity, which is negative in this context.

An object initially at rest accelerates at 1.25 m/s² [N] for 5.50 seconds. What is the final velocity?

• 6.88 m/s [N]

• 5.50 m/s [N]

• 4.87 m/s [N]

• 9.81 m/s [N]

Answer explanation

To find the final velocity, use the formula: final velocity = initial velocity + (acceleration × time). Here, initial velocity = 0, acceleration = 1.25 m/s², and time = 5.50 s. Thus, final velocity = 0 + (1.25 × 5.50) = 6.88 m/s [N].

A book falls off a shelf and reaches a final velocity of 4.87 m/s [down]. If the acceleration due to gravity is 9.81 m/s², how long does it take to fall?

• 0.75 s

• 0.25 s

• 0.50 s

• 0.496 s

Answer explanation

To find the time of fall, use the formula v = g * t. Rearranging gives t = v / g. Substituting v = 4.87 m/s and g = 9.81 m/s² results in t = 0.496 s, confirming the correct answer is 0.496 s.