A 2,000-kilogram sports car accelerates at a rate of 30 meters per second squared. The velocity of the car is v=at, where a is acceleration in meters per second squared, and t is time in seconds. The kinetic energy of the car is KE=12mv2, where m is the mass in kilograms. Which function represents the kinetic energy of the car after accelerating for t seconds?
Answer
A
cap k cap e is equal to 1 comma 000 t squared
B
cap k cap e is equal to 900 comma 000 t squared
Explanation
After t seconds, the car’s velocity is v = at = 30t meters per second. Substitute m = 2,000 and v = 30t into KE = ½mv²: KE = ½(2,000)(30t)² = 1,000 × 900t² = 900,000t². Thus the kinetic energy is 900,000t², matching choice B.
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