A cart travels with a constant, nonzero acceleration along a straight line.

Which of the following graphs best represents the relationship between the distance the cart travels from its starting point and the time of travel? distance vs time

For a cart traveling with **constant acceleration** along a straight line, the relationship between the distance traveled (\(d\)) and the time (\(t\)) is given by the equation:

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

Where:
- \(d\) is the distance traveled,
- \(v_0\) is the initial velocity,
- \(a\) is the constant acceleration,
- \(t\) is the time.

### Key Points:
- If the cart starts from rest (\(v_0 = 0\)), the equation simplifies to \(d = \frac{1}{2} a t^2\).
- The relationship between distance and time is quadratic (\(d \propto t^2\)).

### The Graph:
- The graph of distance versus time will be a **parabolic curve**, since distance increases with the square of time.
- This curve starts at the origin (if the cart starts from rest) and curves upward as time increases.
  
The correct graph would have the shape of a **parabola opening upwards**, representing the increasing rate of change of distance with respect to time.

Would you like further details or have any questions?

Here are 5 related questions for you:
1. How would the graph change if the cart had an initial velocity?
2. How does the slope of a distance vs. time graph relate to velocity?
3. What is the difference between uniform velocity and constant acceleration on a distance-time graph?
4. How would the graph change if the acceleration was negative?
5. How can you calculate the velocity from the distance-time graph?

**Tip:** The area under a velocity-time graph gives the distance traveled over that time period.

A cart travels with a constant, nonzero acceleration along a straight line. Which of the following graphs best represents the relationship between the distance the cart travels from its starting point and the time of travel? distance vs time

Understand how to graph the relationship between distance and time for a cart moving with constant acceleration. Explore key concepts in kinematics, including the quadratic relationship between distance and time, and the relevant kinematic equations. Suitable for students in Grades 9-12.

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