It continues to fly along the same horizontal arc but increases its speed at the rate of

1.41 m/s.Find the magnitude of acceleration under these new conditions.
Answer in units of m/s

You mean NOT m/s

BUT m/s^2

Speed is in meters per second
Acceleration is in meters/second per second (change in speed over time)
so
m/s^2

THAT is really, really important !

now if the direction does not change and the speed remains 1.41 m/s then there is no change in velocity and the acceleration is zero.

IF however you meant to write 1.41 m/s^2 then the acceleration is 1.41 m/s^2

If the plane is circling however then the velocity is changing direction even if the speed is the same

and the centripetal acceleration is
v^2/R

where v is the tangential speed and R is the radius of the turn
This acceleration vector points toward the center of the circle.

To find the magnitude of acceleration, we first need to determine the change in velocity.

Given that the speed is increasing at a rate of 1.41 m/s, we can say that the change in velocity is 1.41 m/s in the horizontal direction.

Now, we need to find the time taken for this change in velocity. Since we are given that the object continues to fly along the same horizontal arc, we can assume that the object moves in a circular path. Therefore, the time taken to complete one full revolution is the period of motion, which we can represent as T.

Next, we'll use the formula for centripetal acceleration:

a = Δv / Δt

Considering that the change in velocity is 1.41 m/s and the time taken for one full revolution is T, we get:

a = 1.41 m/s / T

Since the period (T) of the motion is not given, we need more information to calculate the magnitude of acceleration.

To find the magnitude of acceleration, we need to determine the change in speed over time. This can be found using the formula for acceleration:

acceleration = change in speed / time

In this case, the change in speed is given as 1.41 m/s, and the time is not provided. Therefore, we need to obtain the time in order to calculate the magnitude of acceleration.

Let's assume that the time taken for the speed to increase by 1.41 m/s is one second. This is just an assumption to help illustrate the process.

Now, we can calculate the acceleration using the formula:

acceleration = change in speed / time
acceleration = 1.41 m/s / 1 s
acceleration = 1.41 m/s^2

Therefore, under the new conditions, the magnitude of acceleration is 1.41 m/s^2.