Aball is on a horizontal, flat plane at the orgin of your axis system at t0. the ball has an initial velocity of 1.30m/s along the + y axis and, starting at t0 recieves an acceleration of 2.10 m/s^2 in the + x direction. at t= 2.50s a) what is the position of the ball in terms of its x and y coordinates? b) what is the displacement of the ball? c) what is the velocity of the ball?

It sounds like the ball's velocity along the -axis should be taken to be constant, in which case the ball has velocity vector

We note that at , we're told the ball is at the origin, so its position at this point is . We then integrate the velocity vector to find the position vector:

For the sake of simplicity, I'll assume , so that

(a) Then at , the ball's position in the plane is given by the vector

which is to say its position in the plane is at the point (6.56, 3.25).

(b) The ball's displacement is the same as its position, but in vector form (as above).

(c) The ball has velocity

That is, the ball has a speed of and is traveling in a direction of about relative to the positive -axis.

what is the question because that is not a question.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.