PHYSICS 231
1st Midterm, October 11, 1995, 10:00 am - 10:50 am
Instructor: P. Q. Hung

Do all problems (20 points each). READ them carefully. You have to EXPLAIN all your answers. DO NOT just write them down.

Useful formulas:

I) Laurel running at 10 m/s is 40 m behind Hardy when Hardy starts from rest on his moped with an acceleration 1.0 m/ . How long does it take for Laurel to catch up with Hardy?

Let Laurel's position be given by and Hardy's position by . Then

, and .

When , Laurel has caught up with Hardy. Setting the positions equal gives us

We choose the earlier of these two answers since we want to know when Laurel first catches up with Hardy.

II) The position of a particle as a function of time is

a) What is the shape of the particle's trajectory? Give a quantitative answer.

Taking the magnitude of the vector, we find that

.

Since the magnitude is always 4m, the particle always lies on a circle of radius 4m.

At t=0 s, .

At t=.25 s, .

At t=.5 s, .

At t=.75 s, .

The particle therefore travels clockwise around the circular trajectory.

b) Compute the velocity vector.