The position of a particle moving along the X axis varies in time according to the expression x=3t2 wwhere X is in meters and t is in seconds (a)find its position at t=3s and 3s+t(b)using limiting method find the velocity at t=3s .
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Solution
x=t3+4t2-2t+5
v=
dx
dt
=3t2+8t-2
a=
dv
dt
=6t+8
At t=4s,v=3(4)2+8(4)-2
=78m/s, (i) is O.K.
a=6(4)+8=32m/s2, (ii) is O.K.
t1=0,x1=5m
t2=4s,x2=(4)3+4(4)2-2(4)+5=125m
t=0 to t=4 s,
ˉ
v
=
x2-x1
t2-t1
=4s,
t1=0,v1=-2m/s
t2=4s,v2=3(4)2+8(4)-2=78m/s
t=0 to t=4s
ˉ
a
=
v2-v1
t2-t1
=
78-(-2)
4-0
=20m/s2, (iv) is O.K.
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