Questions: Two cars are moving around a flat curved road, each having the speed of 15 m/s, but moving in the opposite direction from each other. If the radius of the track is 80 m, what are their centripetal accelerations? - both have the same acceleration of 2.81 m/s^2, and directed towards the center of the curve - one has an acceleration of 1.38 m/s^2, directed towards tangential to the curve, and the other has an acceleration of -1.38 m/s^2, directed away from the center - one has an acceleration of 2.81 m/s^2, directed towards the center of the curve, and the other has an acceleration of -2.81 m/s^2, directed tangential to the curve - both have an acceleration of 1.38 m/s^2, directed towards the center of the road

Two cars are moving around a flat curved road, each having the speed of 15 m/s, but moving in the opposite direction from each other. If the radius of the track is 80 m, what are their centripetal accelerations?
- both have the same acceleration of 2.81 m/s^2, and directed towards the center of the curve
- one has an acceleration of 1.38 m/s^2, directed towards tangential to the curve, and the other has an acceleration of -1.38 m/s^2, directed away from the center
- one has an acceleration of 2.81 m/s^2, directed towards the center of the curve, and the other has an acceleration of -2.81 m/s^2, directed tangential to the curve
- both have an acceleration of 1.38 m/s^2, directed towards the center of the road

Transcript text: Two cars are moving around a flat curved road, each having the speed of $15 \mathrm{~m} / \mathrm{s}$, but moving in the opposite direction from each other. If the radius of the track is 80 m , what are their centripetal accelerations? both have the same acceleration of $2.81 \mathrm{~m} / \mathrm{s}^{2}$, and directed towards the center of the curve one has an acceleration of $1.38 \mathrm{~m} / \mathrm{s}^{2}$, directed towards tangential to the curve, and the other has an acceleration of $-1.38 \mathrm{~m} / \mathrm{s}^{2}$, directed away from the center one has an acceleration of $2.81 \mathrm{~m} / \mathrm{s}^{2}$, directed towards the center of the curve, and the other has an acceleration of $-2.81 \mathrm{~m} / \mathrm{s}^{2}$, directed tangential to the curve both have an acceleration of $1.38 \mathrm{~m} / \mathrm{s}^{2}$, directed towards the center of the road

Solution

Solution Steps

Step 1: Understanding the Problem

We need to determine the centripetal accelerations of two cars moving in opposite directions around a flat curved road with a given speed and radius.

Step 2: Formula for Centripetal Acceleration

The formula for centripetal acceleration $a_c$ is given by: \[ a_c = \frac{v^2}{r} \] where $v$ is the speed of the car and $r$ is the radius of the curve.

Step 3: Plugging in the Values

Given:

Speed $v = 15 \, \text{m/s}$
Radius $r = 80 \, \text{m}$

Substitute these values into the formula: \[ a_c = \frac{(15 \, \text{m/s})^2}{80 \, \text{m}} \] \[ a_c = \frac{225 \, \text{m}^2/\text{s}^2}{80 \, \text{m}} \] \[ a_c = 2.8125 \, \text{m/s}^2 \]

Step 4: Rounding to Four Significant Digits

Round the result to four significant digits: \[ a_c = 2.813 \, \text{m/s}^2 \]

Step 5: Direction of Centripetal Acceleration

Centripetal acceleration is always directed towards the center of the curve for both cars, regardless of their direction of travel.