Question

After extensive research, a physicist has developed a way to determine the minimum stopping distance of a car. The stopping distance, ( s ), is greater than or equal to the ratio of the square of the speed of the car, ( u ), to twice the deceleration, ( d ). Which of the following inequalities represents this situation?

a) ( s ≥ frac{u^2}{2d} )
b) ( s ≤frac{u^2}{2d} )
c) ( s > frac{2d}{u^2} )
d) ( s < frac{2d}{u^2} )

Answer 1

The stopping distance of a car is represented by the inequality
`\[ s \geq (u^2)/(2d) \]` . The correct option is a)
`\[ s \geq (u^2)/(2d) \]` .

Step-by-step explanation:

To derive the correct inequality, let's analyze the given information:

"The stopping distance,
`\( s \)`, is greater than or equal to the ratio of the square of the speed of the car,
`\( u \)`, to twice the deceleration,
`\( d \).`"

Mathematically, this can be expressed as:

`\[ s \geq (u^2)/(2d) \]`

Here's how to interpret the inequality:

`\( u^2 \)` : Square of the speed of the car.

`\( 2d \)` : Twice the deceleration.

The ratio of
`\( u^2 \) to \( 2d \)` represents a portion of the stopping distance, and the stopping distance
`(\( s \))` is greater than or equal to this ratio.

Therefore, the correct inequality is
`\( s \geq (u^2)/(2d) \)`, which corresponds to option:

a)
`\( s \geq (u^2)/(2d) \)` .