Astone of mass m is thrown upward at a 30? angle to the horizontal. at the instant the stone reaches its highest point, why is the stone neither gaining nor losing speed?

At highest point of the path the acceleration is perpendicular to velocity direction so there is no change in speed at this moment.

Explanation:

When an object is thrown at an angle of 30 degree with the horizontal with some initial speed

then we will have

now its acceleration due to gravity is given as

with the help of kinematics we can say that its velocity after any time "t" is given as

now when it will reach to its highest point then its velocity in y direction becomes zero

now since final velocity is along x direction only at the highest point while its acceleration at that point is due to gravity so at that moment there is no change in speed.