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The relationship between velocity and kinetic energy is quadratic. The kinetic energy (KE) is given by the equation:

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

Where m represents the mass of the object and v represents its velocity.

If the velocity decreases by 70%, it means the new velocity (v') is equal to 30% of the original velocity (v). Mathematically, this can be expressed as:

v' = 0.3 * v

To find the percentage decrease in kinetic energy, we need to compare the initial kinetic energy (KE) to the final kinetic energy (KE').

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

Final KE' = (1/2) * m * v'^2 = (1/2) * m * (0.3 * v)^2 = (1/2) * m * 0.09 * v^2 = 0.045 * m * v^2

The percentage decrease in kinetic energy can be calculated using the following formula:

Percentage decrease = [(Initial KE - Final KE') / Initial KE] * 100

Substituting the values, we have:

Percentage decrease = [(KE - KE') / KE] * 100 Percentage decrease = [(KE - 0.045 * m * v^2) / KE] * 100

Since we're interested in the percentage decrease, we can simplify the formula by dividing both the numerator and denominator by KE:

Percentage decrease = [(KE / KE) - (0.045 * m * v^2) / KE] * 100 Percentage decrease = [1 - (0.045 * m * v^2) / KE] * 100

Hence, the percentage decrease in kinetic energy when the velocity decreases by 70% is given by the expression [1 - (0.045 * m * v^2) / KE] multiplied by 100.

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