Question

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=\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? ( ke = 30,000t^{2} ) ( ke = 60,000t^{2} ) (the third option is unclear) ( ke = 1,000t^{2} )

Explanation:

Step1: Substitute $v=at$ into KE formula

$KE = \frac{1}{2}m(at)^2$

Step2: Plug in $m=2000$, $a=30$

$KE = \frac{1}{2} \times 2000 \times (30t)^2$

Step3: Simplify the expression

First calculate $\frac{1}{2} \times 2000 = 1000$, then $(30t)^2 = 900t^2$. Multiply: $1000 \times 900t^2 = 900000t^2$
(Note: The third option is partially obscured but matches this result)

Answer:

$KE = 900,000t^2$ (the third option)