A hockey puck slides with an initial speed of 40.7 m/s on a large frozen lake. If the coefficient of kinetic friction between the puck and the ice is 0.038, what is the speed of the puck after 11.9 s?

To find the speed of the hockey puck after 11.9 s, you can use the equation of motion that relates speed, time, and acceleration. The acceleration of the puck can be determined using Newton's second law and the force of friction.

First, let's find the acceleration of the puck due to the frictional force. The frictional force is equal to the coefficient of kinetic friction multiplied by the normal force. In this case, we assume that the normal force is equal to the weight of the puck since it is sliding on a horizontal surface. The formula for the frictional force (F_friction) is given by:

F_friction = μ * N,

where μ is the coefficient of kinetic friction and N is the normal force.

Since the normal force is equal to the weight of the puck (N = m * g), the frictional force can also be written as:

F_friction = μ * m * g,

where m is the mass of the puck and g is the acceleration due to gravity.

Next, we need to calculate the frictional force. To do this, we need to know the mass of the puck. If the mass of the puck is given, you can use it directly in the equation. If not, you will need to find it using other information.

Once you have the value for the frictional force, you can use Newton's second law equation to find the acceleration (a):

F_net = m * a,

where F_net is the net force acting on the puck. In this case, since the puck is sliding on a horizontal surface, the net force is equal to the frictional force:

F_net = F_friction.

Now that you have the acceleration, you can use the motion equation to find the speed of the puck after 11.9 s. The motion equation is:

v = u + a * t,

where v is the final velocity (speed) of the puck, u is the initial velocity of the puck, a is the acceleration, and t is the time.

Using this equation, you can substitute the values you found for the initial velocity, acceleration, and time to calculate the final velocity (speed) of the puck after 11.9 s.