A car is rounding a curve that is the arc of a

circle with a radius of r .
If the car has a constant speed of 10 m/s,
and its acceleration is 5 m/s
2
, what is the
radius of the curve?

The radius is 20 m.

r= v²/a

mnmnmn

To find the radius of the curve, we can make use of the relationship between acceleration, speed, and radius of a curve.

The centripetal acceleration of an object moving in a circular path is given by the formula:

a = (v^2) / r

Where:
a = acceleration
v = velocity (speed)
r = radius of the curve

From the given information:
Speed of the car, v = 10 m/s
Acceleration of the car, a = 5 m/s^2

Substituting the values into the formula, we get:

5 m/s^2 = (10 m/s)^2 / r

To find the radius, we can rearrange the equation:

r = (10 m/s)^2 / 5 m/s^2
r = 100 m^2/s^2 / 5 m/s^2
r = 20 m

Therefore, the radius of the curve is 20 meters.