Problems for Week 2

Examples 3-1 from page 63 in Young and Freedman

Calculating average and instantaneous velocity

You are operating a radio-controlled model car on a vacant tennis court. Your position is the origin of coordinates, and the surface of the court lies in the xy-plane. The car, whcih we represent as a point, has x- and y-coordinates that vary with time according to

(a)

Find the car's coordinates and its distance from you at time t = 2.0 s.

(b)

Find the car's displacement and average velocity during the interval from t = 0 to t = 2.0 s.

(c)

Derive a general expression for the car's instantaneous velocity, and find the instantaneous velocity at time t = 2.0 s.

Note: The solution for this example is given on page 60 in Young.

Problem 3-24 from page 86 in Young and Freedman

The radius of the earth's orbit around the sun (assumed to be circular) is , and the earth travels around this orbit in 365 days.

(a)

What is the magnitude of the orbital velocity of the earth in ?

(b)

What is the radial acceleration of the earth toward the sun in ?