Yes — her scooter can be accelerating, and it is accelerating whenever she is turning. A speedometer reports only the magnitude of her velocity; the direction of that velocity can be changing all the while, and a change in direction alone is already a change in velocity.
What a steady needle actually fixes — the Threads of Curiosity box beside Section $\displaystyle 4.1.4$ (the Average acceleration page) says the speedometer reading is nearly, though not exactly, the magnitude of the velocity at that instant, while it is the way the tyres are pointing that gives the direction of the velocity. So the needle pins down one half of the velocity and says nothing at all about the other half.
Why half is not enough — Eq. (4.3a) defines \(\displaystyle \text{average acceleration} = \frac{\text{change in velocity}}{\text{time interval}} \), and Section $\displaystyle 4.1.4$ states in as many words that this change can come from the magnitude of the velocity, from its direction, or from both. That same paragraph forward-refers to Section $\displaystyle 4.4$ for an example in which the speed stays constant and only the direction changes — which is precisely the situation this question describes.
How, concretely: she must be riding along a curve — a bend in the road, a roundabout, a circular turn, i.e. uniform circular motion. Section $\displaystyle 4.4.1$ reaches it by counting turns: an athlete on a rectangular track changes direction $\displaystyle 4$ times per lap (Fig. 4.23a), on a hexagonal track $\displaystyle 6$ times (Fig. 4.23b), and as the number of sides is increased without limit the track becomes a circle and the direction of the velocity changes continuously (Fig. 4.23c). At each point the velocity lies along the tangent to the path (Fig. $\displaystyle 4.25$), so it points a new way at every instant while its magnitude never moves.
Section $\displaystyle 4.4.1$ then states the conclusion the question is built on: uniform circular motion is accelerated motion, for the single reason that the direction of the velocity keeps changing; and the Note beside it adds that in everyday life we call a vehicle "accelerating" only when its speed changes and routinely fail to notice acceleration that is a change of direction alone. Her scooter is exactly the case that Note is about.
When she would not be accelerating — only if the road is straight as well as her speed steady. Then the initial and final velocities agree in magnitude and direction, and Eq. (4.3c) gives \(\displaystyle a = \frac{v - u}{t} = \frac{10\ \mathrm{m\ s^{-1}} - 10\ \mathrm{m\ s^{-1}}}{t} = 0\ \mathrm{m\ s^{-2}} \) for any time interval (the \(\displaystyle 10\ \mathrm{m\ s^{-1}} \) is only there to show the substitution; any steady reading gives the same zero). The Note in Section $\displaystyle 4.1.4$ makes the same point with a bus on a straight highway — moving fast, yet with zero acceleration.
Marked as reasoning rather than the book's content: the chapter establishes only that this acceleration is non-zero; it never says which way it points, and nothing in Chapter $\displaystyle 4$ mentions an acceleration directed towards the centre of the circle — so a Grade $\displaystyle 9$ answer should not supply a direction here. Similarly, the speedometer box's "nearly, but not exactly" means a perfectly steady needle is a very good indicator of constant speed rather than a strict guarantee of it.
The printed key does not fit this question. The book's Answer Key gives, under Chapter $\displaystyle 4$ → Revise, Reflect, Refine, item 3. Yes, Yes, different — three answers. Question $\displaystyle 3$ as printed is one sentence: a single yes/no ("Is it possible for her scooter to be accelerating") followed by "if so, how?". A how cannot be answered "Yes", and there is nothing in the question that can be answered "different". A three-part entry of exactly that shape does fit Pause and Ponder question $\displaystyle 3$ of the same chapter — the ball on the inclined track of Fig. $\displaystyle 4.6$ — which asks three things in a row: is the motion straight-line motion, can it be depicted on a horizontal line as in Fig. $\displaystyle 4.3$, and are the total distance travelled and the magnitude of displacement equal or different. The Answer Key's Pause and Ponder list for Chapter $\displaystyle 4$ prints only item $\displaystyle 4$, with no item $\displaystyle 3$; and the key does print yes/no answers to Pause and Ponder items in other chapters (Chapter $\displaystyle 7$'s list opens "1. No"), so that gap is not a policy of skipping non-numerical answers. The entry looks set against the wrong list.
So, plainly: the book's printed Answer Key gives "Yes, Yes, different" for this question, which does not agree with the question as printed on the Revise, Reflect, Refine page or with Section $\displaystyle 4.4.1$ read as an answer to it. The chapter's own text settles it the other way — Section $\displaystyle 4.1.4$ counts a change of direction as a change of velocity, and Section $\displaystyle 4.4.1$ declares uniform circular motion accelerated for that reason alone — so the answer is Yes: a scooter held at a constant speedometer reading is accelerating whenever it is going round a bend, and is not accelerating only if it is also going straight. Of the key's three words, only the first one survives.
