Question

A car maintains a speed of 23 mi/h for five seconds it then accelerates to a speed of 46 mi/h in 5 seconds it maintains that speed for the next 5 seconds which graph shows the cars speed over time​

Answer 1

For this case we have three different functions in three different intervals.
Let's write the function for each interval.
We have:
For t = [0,5]
v (t) = 23 m / h
For t = [5,10]
v (t) - vo (t) = m * (t - to)
m = (46-23) / (10-5)
m = 4.6
We choose an ordered pair:
(to, vo (t))) = (5, 23)
Substituting:
v (t) - 23 = (4.6) * (t - 5)
Rewriting:
v (t) - 23 = (4.6) * (t - 5)
v (t) = 4.6 * t - 23 + 23
v (t) = 4.6 * t
For t = [10, 5]
v (t) = 46
Answer:
First graphic (from left to right)

Answer 2

We are given a information that:

A car maintains a speed of 23 mi/h for five seconds it then accelerates to a speed of 46 mi/h in 5 seconds it maintains that speed for the next 5 seconds.

i.e. from 0-5 sec the speed of car is constant i.e. 23 mi/h.

Hence, we will get a straight horizontal line from 0-5 sec.

Then the speed reaches to 46 mi/h at 10 sec and the speed increases continuously.

Then after 10 sec-15 sec it maintains that speed i.e. the speed is again constant between the interval 10-15 i.e. again a horizontal line is obtained in that interval.

The graph is attached to the answer.