It would be 5 m right? because thats when she started slowing down ?

125 m

Explanation:

When given a time vs. velocity graph, the distance travelled will be the area under the curve.

Why? Recall that which relates to the classic equation (total displacement is equal to the average velocity multiplied by the time).

In this case, from 0 seconds to 5 seconds, we have a convenient rectangle. Finding the area of the rectangle is simple, recall that the area of a rectangle is length x width.

The width of the velocity is 25 m/s. This means that the student was driving at a constant speed of 25 m/s the entire time, which means her average velocity for the period of 5 seconds must have been 25 m/s. Perfect.

We want the total distance she travelled from 0 seconds to 5 seconds, which is a total of 5 seconds of driving.

Now multiply:

Therefore, she travelled 125 m during the first five seconds of motion.

*Extra note regarding why 5 m isn't correct:

Remember we are looking at a time vs velocity graph. She starts slowing down at t=5s (5 seconds after she started driving), but that doesn't mean she travelled 5 meters. Imagine you start driving, from rest, at an average velocity of 30 m/s for 10 seconds. Just because you start to slow down 10 seconds after driving doesn't mean you travelled 10 meters. Seconds are not meters! Remember, in a time vs velocity graph, if you want to find total distance travelled from a certain interval, find the area under the curve between that interval.