Question

Entrance and exit ramps for freeways in are often circular stretches of road. As you go around one at a constant speed, you will experience a constant acceleration.. Suppose you drive through an entrance ramp at a modest speed and your acceleration is 3.5m/s2. What will be the acceleration if you triple your speed?

Answer #1

i.e talking about the sideways forces that you experience.

For these accelerations a = w^2 r = v^2 /r (w is the angular
velocity)

v is the linear velocity and r is the radius of the circle.

Now for your question r does not change but we do wish to consider
v.

so a is proportional to v^2

This means that if you double your speed than (a) goes up by the
factor of (2^2) which is 4 times

At three times the speed (a) increases by a factor of (3^2) which
is 9 times greater.

9 times 2.0 m/s^2 is 31.5m/s^2

That is your new acceleration at the quoted speed.

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