A child on a sled reaches the bottom of a hill with a velocity of 10.0m/s and travels 25.0m along a horizontal straightaway to a stop. If the child and sled together have a mass of 60kg, what is the average retarding force on the sled on the horizontal straightaway?.

Vf^2 = Vo^2 + 2a*d = 0.

a = -(Vo^2)/2d = -(10^2)/50 = -2.0 m/s^2

F = M*a = 60 * (-2.0)=-120 N. Retarding force.

THank you

Well, it seems like the sled had a downhill ride and now it's time for the uphill struggle of stopping! Let's calculate the average retarding force.

We can use the equation: force = mass x acceleration.

Given:
Initial velocity (u) = 10.0 m/s
Final velocity (v) = 0 m/s (since the child and sled come to a stop)
Distance (s) = 25.0 m
Mass (m) = 60 kg

First, we need to find the acceleration. We can use the equation v^2 = u^2 + 2as to find it.

Rearranging the equation, we have: a = (v^2 - u^2) / (2s)

a = (0^2 - 10.0^2) / (2 * -25.0) [Negative sign because the sled is decelerating]

Solving that equation, we get a = 4.0 m/s^2.

Now we can calculate the force using the formula: force = mass x acceleration

Force = 60 kg x 4.0 m/s^2

Force = 240 N

So, the average retarding force on the sled on the horizontal straightaway is 240 N. But remember, the force of gravity won't help the sled uphill, unlike a fantasy sled powered by unicorn magic!

To find the average retarding force on the sled on the horizontal straightaway, we can apply Newton's second law of motion.

Newton's second law states that the force acting on an object is equal to the product of its mass and acceleration. In this case, since the sled comes to a stop, the acceleration is in the opposite direction of motion and can be termed a "retarding" force.

The formula representing Newton's second law is:

F = m * a

Where F is the force acting on the object, m is its mass, and a is its acceleration.

In this scenario, the sled's mass is given as 60 kg. We need to find the acceleration to calculate the retarding force. To get the acceleration, we can use the kinematic equation:

v² = u² + 2as

Where v is the final velocity (0 m/s, as the sled comes to a stop), u is the initial velocity (10.0 m/s), a is the acceleration, and s is the displacement (25.0 m).

Rearranging the equation to solve for a:

a = (v² - u²) / (2s)

Substituting the values:

a = (0² - 10.0²) / (2 * 25.0)

a = (-100.0) / 50.0

a = -2.0 m/s²

Now that we have the acceleration, we can calculate the retarding force using Newton's second law:

F = m * a

F = 60 kg * (-2.0 m/s²)

F = -120 N

Therefore, the average retarding force on the sled on the horizontal straightaway is 120 Newtons opposite to the direction of motion.