Question

question 10 (1 point)
a truck weighs twice as much as a car, and is moving at twice the speed of the car.
which statement is true about the trucks kinetic energy compared to that of the
car?

all that can be said is that the truck has more kinetic energy.

the truck has twice the kinetic energy of the car.

the truck has 4 times the kinetic energy of the car.

the truck has 8 times the kinetic energy of the car.

Explanation:

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy (KE) is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is speed.

Step2: Define Variables for Car and Truck

Let the mass of the car be $m_c = m$ and its speed be $v_c = v$. Then the mass of the truck is $m_t = 2m$ (twice the car's mass) and its speed is $v_t = 2v$ (twice the car's speed).

Step3: Calculate KE of Car

For the car, $KE_c = \frac{1}{2}m_cv_c^2 = \frac{1}{2}mv^2$.

Step4: Calculate KE of Truck

For the truck, $KE_t = \frac{1}{2}m_tv_t^2 = \frac{1}{2}(2m)(2v)^2$. Simplify: $\frac{1}{2}(2m)(4v^2) = (m)(4v^2) = 4mv^2$. But from Step3, $\frac{1}{2}mv^2$ is $KE_c$, so $4mv^2 = 8\times(\frac{1}{2}mv^2) = 8KE_c$.

Answer:

The truck has 8 times the kinetic energy of the car. (Corresponding option: The truck has 8 times the kinetic energy of the car.)