A car takes a turn with the radius of 150 m at the speed of 30m/s.

a) Calculate the acceleration at 60 degree angle around the curve.

the answer is 5.7m/s2,

What formula do I use ?

To calculate the acceleration of a car taking a turn, you can use the centripetal acceleration formula. Centripetal acceleration is the acceleration directed toward the center of the circular path that the car is following.

The formula for centripetal acceleration is given by:

ac = v^2 / r

where:
- ac is the centripetal acceleration
- v is the velocity of the car
- r is the radius of the turn

In this case, the velocity of the car is given as 30 m/s, and the radius of the turn is given as 150 m.

So, by substituting these values into the formula, you can calculate the centripetal acceleration as follows:

ac = (30 m/s)^2 / 150 m

Simplifying the equation:

ac = 900 m^2/s^2 / 150 m

ac = 6 m/s^2

However, the question asks for the acceleration at a 60-degree angle around the curve. This means you need to find the component of acceleration in the direction perpendicular to the velocity vector.

Since the car is taking a curved turn, the acceleration can be broken down into two components: tangential acceleration (at) and normal acceleration (an).

The tangential acceleration (at) describes the change in the magnitude of the velocity vector, while the normal acceleration (an) describes the change in direction of the velocity vector.

To find the normal acceleration at a 60-degree angle, you need to multiply the centripetal acceleration by the sine of the angle:

an = ac * sin(60°)

Using the given centripetal acceleration value of 6 m/s^2:

an = 6 m/s^2 * sin(60°)

an = 6 m/s^2 * 0.866

an ≈ 5.2 m/s^2

Therefore, the normal acceleration at a 60-degree angle around the curve is approximately 5.2 m/s^2.