a 1520 kg car in motion rolls down a frictionless hill that is inclined at 14.4°. what is the acceleration…

Explanation:

Step1: Analyze the force acting on the car

The gravitational - force component along the incline provides the acceleration. The gravitational force is $F = mg$, and the component of the gravitational force along the incline is $F_{x}=mg\sin\theta$, where $m$ is the mass of the car, $g = 9.8\ m/s^{2}$ is the acceleration due to gravity, and $\theta$ is the angle of the incline. According to Newton's second - law $F = ma$, and in this case $F_{x}=ma$. So $mg\sin\theta=ma$.

Step2: Solve for the acceleration

We can cancel out the mass $m$ from both sides of the equation $mg\sin\theta=ma$. We get $a = g\sin\theta$. Substitute $g = 9.8\ m/s^{2}$ and $\theta = 14.4^{\circ}$ into the formula. $\sin(14.4^{\circ})\approx0.248$. Then $a=9.8\times0.248\ m/s^{2}$. $a\approx2.43\ m/s^{2}$

Answer:

$2.43$