3.
in order for acceleration of an object to occur, the sum of the forces must be

a. fractions

b. zero

c. anything but zero

d. decimals

In order for acceleration of an object to occur, the sum of the forces must be anything but zero.

Option C

Explanation:

Based on Newton second laws of motion, the acceleration due to gravity of any object is directly proportional to the net force acting on the object and inversely proportional to the mass of the object. So, the sum of all the forces acting on the object will decide the acceleration attained by the object.

If the total forces are zero then the acceleration of the object will be zero. In case of deceleration, the net force would be having negative sign and thus increase in net force will lead to increase in acceleration.  Hence, for the occurrence of acceleration, the total forces sum would be anything but zero.

Work is equal to a force over a distance and is equal to the change in kinetic energy, so

- Fd=ΔKE
−Fd=1/2mv22−1/2mv21
d=(1/2mv22−1/2mv21)/−F

We know that Ffric=kFnatural and Fnatural=mg so:

d=(1/2mv22−1/2mv21)/−(k∗mg)d=(−1/2v21)/−(k∗g)

d=(−1/2×(14.6m/s)2)/−(0.137×9.8m/s)

d = 78.9m