Question

test information
description: show all you work, including units, on separate paper. follow the “problem solving method”.
this final exam is cumulative and covers material from the entire course.
instructions: from the list of choices, select the one best answer.
multiple attempts not allowed. this test can only be taken once.
force completion this test can be saved and resumed later.
your answers are saved automatically.
question completion status:
... (question numbers and status icons)
question 28 of 62
a car traveling at 15 m/s follows a curve in the road so that its centripetal acceleration is 7.5 m/s². what is the radius of the curve?
○ 30 m
○ 110 m
○ 45 m
○ 150 m

Explanation:

Step1: Recall centripetal acceleration formula

The formula for centripetal acceleration is \( a_c = \frac{v^2}{r} \), where \( a_c \) is centripetal acceleration, \( v \) is velocity, and \( r \) is the radius of the curve.

Step2: Rearrange formula to solve for \( r \)

Rearranging the formula \( a_c = \frac{v^2}{r} \) for \( r \), we get \( r = \frac{v^2}{a_c} \).

Step3: Substitute given values

We know \( v = 15 \, \text{m/s} \) and \( a_c = 7.5 \, \text{m/s}^2 \). Substituting these values into the formula: \( r = \frac{(15)^2}{7.5} \).

Step4: Calculate the value

First, calculate \( (15)^2 = 225 \). Then, divide by \( 7.5 \): \( \frac{225}{7.5} = 30 \). So the radius \( r = 30 \, \text{m} \).

Answer:

30 m (corresponding to the option "30 m")