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.