Question

a 2000-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 = \frac{1}{2}mv^2 ), where ( m ) is the mass in kilograms. which function represents the kinetic energy of the car after accelerating for ( t ) seconds? ( \bigcirc ke = 100t^2 ) ( \bigcirc ke = 30,000t^2 ) ( \bigcirc ke = 60,000t^2 ) ( \bigcirc ke = 900,000t^2 )

Explanation:

Step1: Substitute \( v = at \) into \( KE = \frac{1}{2}mv^2 \)

Given \( v = at \), substitute this into the kinetic energy formula: \( KE = \frac{1}{2}m(at)^2 \)

Step2: Plug in \( m = 2000 \) and \( a = 30 \)

Substitute \( m = 2000 \) kg and \( a = 30 \) m/s² into the formula:
\( KE = \frac{1}{2} \times 2000 \times (30t)^2 \)
First, calculate \( (30t)^2 = 900t^2 \). Then:
\( KE = \frac{1}{2} \times 2000 \times 900t^2 \)
\( \frac{1}{2} \times 2000 = 1000 \), so:
\( KE = 1000 \times 900t^2 = 900000t^2 \)

Answer:

\( KE = 900,000t^2 \) (the last option, e.g., if options are labeled as D: \( KE = 900,000t^2 \), then D. \( KE = 900,000t^2 \))