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.
[tex]\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][/tex]
Graph the data. See included image.
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:
[tex]x = x_{o} + v_{o}\cdot t + \frac{1}{2}\cdot a\cdot t^{2}[/tex] (1)
Where:
[tex]x_{o}[/tex] - Initial position, in meters.
[tex]x[/tex] - Final position, in meters.
[tex]v_{o}[/tex] - Initial speed, in meters per second.
[tex]t[/tex] - Time, in seconds.
[tex]a[/tex] - Acceleration, in meters per square second.
If we know that [tex]x_{o} = 0\,m[/tex], [tex]v_{o} = 5\,\frac{m}{s}[/tex] and [tex]a = 2.5\,\frac{m}{s^{2}}[/tex], then we derive the formula and obtain all set of ordered pairs:
[tex]x = 5\cdot t +1.25\cdot t^{2}[/tex] (1b)
t = 0 s.
[tex](t, x) = (0\,s, 0\,m)[/tex]
t = 1 s.
[tex](t, x) = (1\,s, 6.25\,m)[/tex]
t = 2 s.
[tex](t, x) = (2\,s, 15\,m)[/tex]
t = 3 s.
[tex](t, x) = (3\,s, 26.25\,m)[/tex]
t = 4 s.
[tex](t, x) = (4\,s, 40\,m)[/tex]
t = 5 s.
[tex](t,x) = (5\,s, 56.25\,m)[/tex]
Now create the graph, which is included below as an attachment.
We kindly invite to check this question on uniform accelerated motion: https://brainly.com/question/12920060
