The expected value of the acceleration of a car on a frictionless track inclined at 9° is 1.535 m/s², calculated using the formula a = g × sin(θ) with g being the acceleration due to gravity.
To calculate the expected value of acceleration of a car on a frictionless track inclined at an angle (θ) of 9°, we can use the formula derived from Newton's second law of motion and the component of gravitational acceleration along the incline. The formula for the acceleration (a) along the incline is a = g × sin(θ), where g is the acceleration due to gravity (approximately 9.81 m/s2). Since there is no friction to resist the car's motion, the entire component of the gravitational force along the slope will be responsible for the car's acceleration.
Using the values given:
g: 9.81 m/s2
θ: 9°
The acceleration (a) can be calculated by plugging these values into the formula:
a = 9.81 m/s2 × sin(9°)
To solve for the acceleration, we first convert the angle from degrees to radians if necessary, then take the sine of the angle, and multiply by the gravitational acceleration.
Therefore, the expected value of the car's acceleration on the inclined plane is 1.535 m/s2 when rounded to three decimal places.