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Chapter2kinematics

By Sarah Tucker,2015-03-30 19:34
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Chapter2kinematicsChapte

    Chapter 2 Kinematics

    2-1. Air resistance acting on a falling body can be taken by the approximate relation for the acceleration: where k is a constant. agkv,?

    Derive a formula for the velocity of the body as a function of time assuming it stars from rest (v=0 at t=0).

    at22-2. The acceleration of a particle is given by . At t=0, v=10m/s and

    x=0 (a) What is the speed as a function of time? (b) What is the displacement as a function of time? (c) What are the acceleration, speed and displacement at t=5.0s?

2-3. The position of a particle as a function of time is given by ;;;;2. Determine the particle’s velocity and acceleration rtijtkm,??7.608.85;;

    as a function of time.

2-4. At t=0, a particle stars from rest and moves in the xy plane with an ;;;2acceleration . Determine (a) the x and y components of aijms,?4.03.0/;;

    velocity. (b) The speed of the particle, and (c) the position of the particle, all as a function of time.

2-5. The position of a particle moving in the xy plane is given by ;;;, where r is in meter and t is in second. (a) Show that rtitj,?2cos32sin3 ;;

    this represents circular motion of radius 2m centered at the origin. (b) Determine the velocity and acceleration vectors as function of time. (c) Determine the speed and magnitude of the acceleration. (d) Show that the acceleration vector always points toward the center of the circle.

    2-6. A swimmer is capable of swimming 1.00m/s in still water. (a) If she aims her body directly across a 75m wide river whose current is 0.80m/s, how far downstream (from a point opposite her starting point) will she land? (b) How long will it take her to reach the other side?

Ans

    2-1 g kt(1)ek

    845/22-2 (a) (b) 3/2xttm,?10()vtms,?10(/)153

    2 (c) amsvmsxm,,,4.5 /25 /80 .;;

    ;;;;;

    vitk 7.602,?2-3 ; 2ak,?

    ;;;22rtitjm,?2.01.5() 2-4 (a) vt3 (b) 5t (c) vt4yx

    ;;;2-5 (b) ; vtitj,??6.0sin3.06.0cos3.0;;; atitj,??18.0sin3.018.0cos3.0

    2(c) vms6.0/ams18.0/

    ;;ar,?9.0(d) Hint:

    2-6 (a) 60m (b)75s

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