Chapter 02, Problem 018 The position of a particle moving along an x axis is giv

Question

Chapter 02, Problem 018 The position of a particle moving along an x axis is given by x- 16.02-3., where x is in meters and t is in seconds Determine (a) the postion, th) the velocity, and (o) the aceeration o err-heiv. Or, le the particle and (g) at what time is it reached? (h) what s th·aceeleration of the partide it te n ant th particle between t-0 andt4.00 s partide snot mo ng (ther nan ate-oro Units 1 Units Ca) Number (b) Number (c) Number (d) Number (e) Number (0) Number (a) Number Ch) Number (0) Number Units nits Units D Units Units units units y accessang thi. Queston Assistance, you wa learn ile you earn point, based on the Pent Potential Poley set by yu,Nruct". Question Allempts: 0 of 10 used oRL

Explanation / Answer

x = 16t^2-3t^3

v = dx/dt = 32t - 9t^2

a = dv/dt = 32-18t

a)

at t = 4
x = 64m

b)

at t = 4 ; v = -16 m/s

c)

at t = 4; a = -40 m/s^2

e)

at max X, dx/dt = 0

32t-9t^2 = 0
t = 32/9 = 3.56 s

d)

Xmax = 67.42m

g)

V is max at a = 0

32-18t = 0
t = 1.78 s

f)

Vmax = 28.44 m/s

h)

when v = 0 ; t = 3.56 sec

a = -32.08 m/s^2

i)

Vavg = dist / time = 64/4 = 16m/s

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