Ask a New Question
Menu

Use this graph of velocity vs. time for two objects to answer the question.

Which statement makes an accurate comparison of the motions for objects C and D?

Responses:

Objects C and D have different accelerations but the same velocity throughout the motion.

Object D has an acceleration that is greater than the acceleration for C.

Objects C and D have different velocities but the same acceleration.

Object C has an acceleration that is greater than the acceleration for D.

7 answers

To accurately compare the motions of objects C and D using a velocity vs. time graph, we need to examine the slopes of the lines representing their velocities over time.

  1. If the lines are horizontal (constant velocity), then both objects have the same velocity throughout the motion.
  2. If one line has a steeper slope than the other, the object corresponding to that line has a greater acceleration.
  3. If the lines cross and are at different heights, the two objects have different velocities but may have the same acceleration if they have the same slope.

Without the actual graph, I can speculate based on common scenarios:

  • If both objects are moving with constant velocity (horizontal lines), then the first statement might be true.
  • If one object's velocity line has a steeper slope than the other, then the acceleration statement would be applicable.

Based on typical scenarios regarding acceleration:

  • If the graph indicates that object D's line is steeper, then "Object D has an acceleration that is greater than the acceleration for C" would be true.
  • Conversely, if C's line is the steeper one, then "Object C has an acceleration that is greater than the acceleration for D" would be accurate.

Considering these possibilities, you would need to refer back to the specific details in your graph to select the most accurate comparative statement.

Use the equation for motion to answer the question.
x=x0+v0t+1/2at^2
An object has a starting position of 2 m, a starting velocity of 15 m/s, and is moving at a constant speed. Which option shows the final position of the object after 1 s?

Responses:

32 m

17 m

60 m

30 m

Given the equation for motion:

\[ x = x_0 + v_0 t + \frac{1}{2} a t^2 \]

where:

  • \( x \) is the final position,
  • \( x_0 \) is the starting position,
  • \( v_0 \) is the starting velocity,
  • \( a \) is the acceleration,
  • \( t \) is the time.

In your scenario:

  • \( x_0 = 2 , \text{m} \) (starting position),
  • \( v_0 = 15 , \text{m/s} \) (starting velocity),
  • The object is moving at a constant speed, which means acceleration \( a = 0 \).
  • \( t = 1 , \text{s} \).

Since the object is moving at a constant speed, the equation simplifies to:

\[ x = x_0 + v_0 t \]

Substituting in the values:

\[ x = 2 , \text{m} + (15 , \text{m/s} \cdot 1 , \text{s}) \] \[ x = 2 , \text{m} + 15 , \text{m} \] \[ x = 17 , \text{m} \]

Therefore, the final position of the object after 1 second is 17 m.

The graph of an object's position over time is a horizontal line and y is not equal to 0. What must be true about the object's motion?
Responses:

The acceleration is negative.

The velocity is zero.

The acceleration is constant and non-zero.

The velocity is constant and non-zero.

If the graph of an object's position over time is a horizontal line (and \( y \) is not equal to 0), this indicates that the position of the object does not change with time.

Here’s what this means for the object's motion:

  1. Position is constant: If the position is constant, it means the object is not moving.
  2. Velocity: Since the position is not changing over time, the velocity of the object is zero (velocity is defined as the change in position over time).
  3. Acceleration: Since the velocity is zero and there is no change in position, the acceleration of the object is also zero.

Based on these points, the correct response is:

The velocity is zero.

Therefore, that is the only statement that must be true about the object's motion in this scenario.

A object travels at constant negative acceleration. What does the graph of the object's velocity as a function of time look like?
Responses:

a curved line increasing from left to right

a curved line decreasing from left to right

a straight line with positive slope

a straight line with negative slope

When an object travels at a constant negative acceleration, it means the object's velocity is decreasing over time. In the context of a velocity vs. time graph:

  1. Negative acceleration indicates that velocity is decreasing.
  2. Since the acceleration is constant, the graph will be linear (not curved).
  3. The line will slant downward (to the left) because the velocity is decreasing over time.

Therefore, the correct response describing the graph of the object's velocity as a function of time is:

a straight line with negative slope.