Howard the soda jerk at Bea's diner slides a 0.60-kg root beer from the end of the counter to a thr=irst customer. A force of friction of 1.2 N brings the drink to a stop right in front of the customer.

Answer 1

To find the acceleration of the root beer, we can first use Newton's second law, which states that the force acting on an object equals its mass times its acceleration:

F = m * a

where F is the force, m is the mass, and a is the acceleration. The force acting on the root beer is the force of friction, which is 1.2 N. We also know the mass of the root beer is 0.60 kg.

1.2 N = 0.60 kg * a

To solve for acceleration, divide both sides by the mass:

a = 1.2 N / 0.60 kg = 2 m/s^2

The acceleration of the root beer is 2 m/s^2. Since the force of friction is acting against the motion of the root beer, its acceleration is negative, which means it is decelerating.

Now, we can use the following kinematic equation to find the initial velocity (v0) of the root beer:

v^2 = v0^2 + 2 * a * d

where v is the final velocity (0 m/s, because the root beer stops), v0 is the initial velocity, a is the acceleration (-2 m/s^2), and d is the distance the root beer traveled.

0 = v0^2 + 2 * (-2 m/s^2) * d

To find the distance, we'll first rearrange the equation to solve for d:

d = (v^2 - v0^2) / (2 * a)

Since we don't know the initial velocity, we can't find the exact distance the root beer traveled. However, this equation can be used to find the distance once the initial velocity is known.