PStep before striking the floor of the lower landing ILlt The marble will no Pla

Question

PStep before striking the floor of the lower landing ILlt The marble will no Place a penny at the corner of a table as shown in verhead view in Figure TP4.2. Place a ruler next to the 2. penny and another penny on the top of the part of the ruler Figure TP4.2 Problems Se the Preface for an esplanation of the icoms used in this problems st For additional assessment iüems Jfor this section, gtoWEBASSIGN of velocity of the object at t = 0, (b) Determine the com- ponents of acceleration of the object at t0. (c) Write expressions for the position vector, the velocity vector and the acceleration vector of the object at any time t 0. (d) Describe the path of the object in an xy plot. SECTION 4.1 The Position, Velocity, and Acceleration Vectors 1.) Suppose the position vector for a particle is given as a func- tion of time by r(1-x(1)i + y(t)J, with x(t) = at + b and y() of + d, where a-1.00 m/s, b-1.00 m, c 0.125 m/s, SECTION 4.2 Two-Dimensional Motion and d 1.00 m. (a) Calculate the average velocity during with Constant Acceleration the time interval from-2.00s to4.00s. (b) Determine. the velocity and the speed at-2.00s. 3. The vector position of a particle varies in time according to V the expression 3.0oi - 6.00e]. where is in meters and RE with time according to the equations x =-5.00 sin , and meters, and t is in seconds. (a) Determine the components 2 The coordinates of an object moving in the sy plane vary y 4.00 5.00 cos wt, where w is a constant, x and y are in t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (b) Determine the accelera- tion of the particle as a function of time. (c) Calculate the particle's position and velocity at t-1.00s

Explanation / Answer

23

a)

v = speed = 3 m/s

r = radius = 2 m

centripetal acceleration is given as

a = v2/r = 32/2 = 4.5 m/s2

yes it can have a net acceleration of 6 m/s2 by having some amount of tangential acceleration.

b)

since ac = 4.5 m/s2 , net acceleration can not be smaller than centrieptal acceleration.

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