A3.00-kg block starts from rest at the top of a 33.0° incline and slides 2.00 m down the incline in 1.80 s. (a) find the acceleration of the block. 1.23 correct: your answer is correct. m/s2 (b) find the coefficient of kinetic friction between the block and the incline. 23 incorrect: your answer is incorrect. (c) find the frictional force acting on the block. n (d) find the speed of the block after it has slid 2.00 m.

(a)

Let's analyze the motion along the direction of the incline. We have:

- distance covered: d = 2.00 m

- time taken: t = 1.80 s

- initial velocity: u = 0

- acceleration: a

We can use the following SUVAT equation:

Since u=0 (the block starts from rest), it becomes

So by solving the equation for a, we find the acceleration:

(b) 0.50

There are two forces acting on the block along the direction of the incline:

- The component of the weight parallel to the surface of the incline:

where

m = 3.00 kg is the mass of the block

g = 9.8 m/s^2 is the acceleration due to gravity

is the angle of the incline

This force is directed down along the slope

- The frictional force, given by

where

is the coefficient of kinetic friction

According to Newton's second law, the resultant of the forces is equal to the product between mass and acceleration:

Solving for , we find

(c) 12.3 N

The frictional force acting on the block is given by

where

is the coefficient of kinetic friction

m = 3.00 kg is the mass of the block

g = 9.8 m/s^2 is the acceleration of gravity

is the angle of the incline

Substituting, we find

(d) 6.26 m/s

The motion along the surface of the incline is an accelerated motion, so we can use the following SUVAT equation

where

v is the final speed of the block

u = 0 is the initial speed

a = 1.23 m/s^2 is the acceleration

d = 2.00 m is the distance covered

Solving the equation for v, we find the speed of the block after 2.00 m: