Studdy AI Logo
Math

Question10. A car experiences a centripetal acceleration of 4.4 m/s24.4 \mathrm{~m} / \mathrm{s}^{2} as it rounds a corner with a speed of 15 m/s15 \mathrm{~m} / \mathrm{s}. What is the radius of the corner? (51.12m)

Studdy Solution

STEP 1

1. The car is moving in a circular path.
2. The centripetal acceleration is 4.4 m/s2 4.4 \, \mathrm{m/s}^2 .
3. The speed of the car is 15 m/s 15 \, \mathrm{m/s} .

STEP 2

1. Recall the formula for centripetal acceleration.
2. Rearrange the formula to solve for the radius.
3. Substitute the given values.
4. Calculate the radius.

STEP 3

Recall the formula for centripetal acceleration:
ac=v2r a_c = \frac{v^2}{r}
where ac a_c is the centripetal acceleration, v v is the speed, and r r is the radius of the circular path.

STEP 4

Rearrange the formula to solve for the radius r r :
r=v2ac r = \frac{v^2}{a_c}

STEP 5

Substitute the given values into the formula:
r=(15 m/s)24.4 m/s2 r = \frac{(15 \, \mathrm{m/s})^2}{4.4 \, \mathrm{m/s}^2}

STEP 6

Calculate the radius:
r=225 m2/s24.4 m/s2 r = \frac{225 \, \mathrm{m}^2/\mathrm{s}^2}{4.4 \, \mathrm{m/s}^2} r≈51.14 m r \approx 51.14 \, \mathrm{m}
The radius of the corner is approximately:
51.14 m \boxed{51.14 \, \mathrm{m}}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord