a racing dog is initially running at 10.0 m/s, but is slowing down. (a) How fast is the dog moving when its kinetic energy has been reduced by half?

To determine how fast the dog is moving when its kinetic energy is reduced by half, we need to use the equation for kinetic energy.

The formula for kinetic energy (KE) is given by:

KE = (1/2) * m * v^2

where m is the mass of the object and v is its velocity. Assuming the mass remains constant, we can simplify the equation to:

KE = (1/2) * v^2

Since we want to find the speed (v) when the kinetic energy is reduced by half, we can set up the following equation:

(1/2) * v^2 = (1/2) * (10.0 m/s)^2

To solve for v, we can cancel out the factor of (1/2) on both sides of the equation:

v^2 = (10.0 m/s)^2

Now, we can take the square root of both sides to solve for v:

v = √((10.0 m/s)^2)

Calculating this, we find:

v ≈ 10.0 m/s

Therefore, the dog would still be moving at approximately 10.0 m/s when its kinetic energy has been reduced by half.

if 1/2 mv^2 is 1/2 of what it was, then veloicy must be sqrt(1/2) of what it was.