Question

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

Answer 1

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

Answer 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.