In this example the acceleration is caused by a friction force. A counter attendant in a diner shoves a ketchup bottle with mass 0.20kg along a smooth, level lunch counter. The bottle leaves her hand with an initial velocity of 2.8m/s. As it slides, it slows down because of the horizontal friction force exerted on it by the countertop. The bottle slides a distance of 1.0m before coming to rest. What are

Magnitude of friction = 0.784 N

The direction = negative X direction.

Explanation:

Given that the acceleration is caused by a friction force. A counter attendant in a diner shoves a ketchup bottle with mass 0.20kg along a smooth, level lunch counter. The bottle leaves her hand with an initial velocity of 2.8m/s. As it slides, it slows down because of the horizontal friction force exerted on it by the countertop. The bottle slides a distance of 1.0m before coming to rest.

The given parameters are;

Mass m = 0.2 kg

Initial velocity U = 2.8 m/s

Distance S = 1.0 m

Let's first calculate the acceleration of the bottle as it slide by using the third equation of motion

V^2 = U^2 - 2as

As the bottle is going to rest, the final velocity V = 0

0 = 2.8^2 - 2 × a × 1

2a = 7.84

a = 7.84/2

a = 3.92 m/s^2

The frictional force F = ma

Substitute a and mass m into the formula

-F = 0.2 × 3.92

F = -784 N

Therefore, the magnitude of the frictional force is 784 N and the direction is in negative x direction.

it should be -8.6 cm hope this out