An object is subjected to retardation, dv/dt = -5√v ,which has initial velocity of 4m/s. The time taken by the object to come to rest would be
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a = dv/dt = -5√v
instantaneous acceleration = -5√v
Acceleration
= ∫-5√v dv
= -5∫v¹'² dv
= -5 . v³'²/3/2
= -5 v³'²x 2 /3 = -10v³'²/3
we know
v = u + at
0 = 4 + -10v³'²/3. t
-4 = -10v³'²/3. t
-4/-10v³'²/3 = t
-12 / -10v³'² = t
instantaneous acceleration = -5√v
Acceleration
= ∫-5√v dv
= -5∫v¹'² dv
= -5 . v³'²/3/2
= -5 v³'²x 2 /3 = -10v³'²/3
we know
v = u + at
0 = 4 + -10v³'²/3. t
-4 = -10v³'²/3. t
-4/-10v³'²/3 = t
-12 / -10v³'² = t
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