Acceleration is the rate of change of velocity over time. The diagram that shows the effect of cutting acceleration by half without changing initial velocity is graph (c)
The equation is given as:
[tex]v = 2t + 4[/tex]
The first equation of motion is:
[tex]v = u + at[/tex]
By comparing both equations, we have:
[tex]u = 4[/tex] --- initial velocity
[tex]a = 2[/tex] --- acceleration
When the acceleration is cut in half, the new acceleration is:
[tex]a_{new} = \frac a2[/tex]
[tex]a_{new} = \frac 22[/tex]
[tex]a_{new} = 1[/tex]
So, the equation of velocity is:
[tex]v = u + at[/tex]
[tex]v = 4 + 1 \times t[/tex]
[tex]v = 4 + t[/tex]
When [tex]t = 0[/tex]
[tex]v = 4 + 0 = 4[/tex]
When [tex]t = 1[/tex]
[tex]v = 4 + 1 = 5[/tex]
The graph of velocity that satisfies [tex]v = 4 + t[/tex] and the values of time (t) and velocity (v) tested above is (c).
See attachment for the diagram (graph)
Read more about velocity and acceleration at:
https://brainly.com/question/2239252