r represents the pos vector of a particle and ω and a are non zero contants
(contant mag includes a zero mag)
A)r=cos(ωt)i +sin(ωt)j + (at)k
B)r=5cos(ωt)i +5sin(ωt)j
C)r=(5at2)i +(2at)j
D)r=5[cos(ωt2)i +sin(ωt2)j]
p)constant speed
q)helical motion
r)constant mag of tangential acceleration
s)constant mag of total acceleration
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1 Answers
106(A) x=cos(wt)
y = sin(wt)
z=at
=> x2+y2=1
Vx = -wsin(wt)
Vy = wcos(wt)
Vz = a
So V = √ΣV2 = √w2+a2 = const
ax = -w2cos(wt)
ay = -w2sin(wt)
az = 0
a = w = const.
tangential acceleration = ldvdtl = w..
of course here as Vz = const.. it is helical motion
you can do similarly for other parts
