Problem 3.

You are driving along an empty straight road at a constant speed u. At some point you notice a tall wall at a distance D in front of you. Would it require a larger force to (a) continue moving straight and decelerate to a full stop before the wall, or (b) turn left or right to avoid the wall? (to make the calculation easier assume that the turn is done at a constant speed along a circular path).

Solution:

(a) If the car continue moving straight then the acceleration should satisfy the following equation:

where - final velocity, which is 0, since the car should stop just before the wall. - initial velocity, which is equal to u. Then

If the mass of the car is m, then the force required to stop the car is

(b) Now the car is turning left or right to avoid the wall. This is the uniform circular motion with a radius D. The acceleration of this motion is

Then the force required to turn the car is

We can see that in the case (a) the force is 2 times smaller.