On an otherwise straight stretch of road near Moffat, Colorado, the road suddenly turns. This bend in the road is a segment of a circle with radius 118 m. Drivers are cautioned to slow down to 45mph as they navigate the curve.

you heed the sign and slow to 45mph , what will be your acceleration going around the curve at this constant speed?

To find the acceleration when going around a curve at a constant speed, we need to use the formula for centripetal acceleration.

The formula for centripetal acceleration is given by:
a = (v^2) / r

Where:
a = centripetal acceleration
v = velocity
r = radius of the curve

In this case, the radius of the curve is given as 118 m and the speed is 45 mph. However, we need to convert the speed from mph to m/s, as the units need to match in the formula.

1 mph = 0.44704 m/s

So, we have:
v = 45 mph * 0.44704 m/s
v ≈ 20.12 m/s

Now we can calculate the centripetal acceleration using the formula:
a = (20.12^2) / 118

Calculating the value:
a ≈ (404.41) / 118
a ≈ 3.43 m/s^2

Therefore, when you slow down to 45 mph and navigate the curve, your acceleration will be approximately 3.43 m/s^2.