1. A ball rolls with a constant acceleration of 2.5 m/s^2 for 5.0 s with an initial velocity of 5.0 m/s. Calculate the ball’s distance from the starting point at 1.0 s intervals. Make a position-time graph for the object’s motion. In your response, show what you are given, the equation that you used, any algebra/work required, a table of data, and your graph. Does anybody know how to solve this question? i need help understanding how to solve it.

In this exercise we derive a kinematic formula, create an arbitrary set of points and introduce the resulting curve on a Cartesian plane.

Physically speaking, this ball experiments an uniform acceleration, that is, its velocity changes uniformly in time. In this question we are going to apply this procedure:

1) Derive the kinematic formula for the position of a ball accelerated uniformly in time.

2) Create an arbitrary set of distinct ordered pairs with the position of the ball in time.

3) Set every point on a Cartesian plane.

4) Create the curve by matching all points.

The equation for the position of the ball in time is:

(1)

Where:

- Initial position, in meters.

- Final position, in meters.

- Initial speed, in meters per second.

- Time, in seconds.

- Acceleration, in meters per square second.

If we know that , and , then we derive the formula and obtain all set of ordered pairs:

(1b)

t = 0 s.

t = 1 s.

t = 2 s.

t = 3 s.

t = 4 s.

t = 5 s.

Now create the graph, which is included below as an attachment.

We kindly invite to check this question on uniform accelerated motion: link

Explanation:

Given:

v₀ = 5.0 m/s

a = 2.5 m/s²

Equation:

Δx = v₀ t + ½ at²

Δx = (5.0 m/s) t + ½ (2.5 m/s²) t²

Δx = 5t + 1.25t²

Make a table of data using 1.0 increments for t.

Graph the data.  See included image.

true tan speed = ang vel x radius