Physics, 02.10.2020 14:01 macybarham

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.

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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:

$x = x_{o} + v_{o}\cdot t + \frac{1}{2}\cdot a\cdot t^{2}$ (1)

Where:

$x_{o}$ - Initial position, in meters.

- Final position, in meters.

$v_{o}$ - Initial speed, in meters per second.

- Time, in seconds.

- Acceleration, in meters per square second.

If we know that $x_{o} = 0\,m$ , $v_{o} = 5\,\frac{m}{s}$ and $a = 2.5\,\frac{m}{s^{2}}$ , then we derive the formula and obtain all set of ordered pairs:

$x = 5\cdot t +1.25\cdot t^{2}$ (1b)

t = 0 s.

$(t, x) = (0\,s, 0\,m)$

t = 1 s.

$(t, x) = (1\,s, 6.25\,m)$

t = 2 s.

$(t, x) = (2\,s, 15\,m)$

t = 3 s.

$(t, x) = (3\,s, 26.25\,m)$

t = 4 s.

$(t, x) = (4\,s, 40\,m)$

t = 5 s.

$(t,x) = (5\,s, 56.25\,m)$

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

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

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

Answer from: kamdenburr

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.

$\left[\begin{array}{cc}t&\Delta x\\0&0\\1.0&6.25\\2.0&15.00\\3.0&26.25\\4.0&40.00\\5.0&56.25\end{array}\right]$

Graph the data. See included image.

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Answer from: Quest

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