Two particles are moving with positions given by x= 4t^2−2t and x= 6t^3+8t respectively.

Explanation:

a)Which of the two has uniform acceleration?

Acceleration is the second derivative of position.  The acceleration of the first particle is:

x = 4t² − 2t

v = 8t − 2

a = 8

The acceleration of the second particle is:

x = 6t³ + 8t

v = 18t² + 8

a = 36t

The first particle has uniform acceleration.

b)Which one is likely to come to rest at some time during its motion?

The particles come to rest when v = 0.  The first particle's velocity has a real zero at t = 4.  The second particle's velocity has only imaginary zeros, meaning v is never 0.

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.