A rocket accelerates on it\'s journey according to the following equation: a(t)=

Question

A rocket accelerates on it's journey according to the following equation: a(t)= te2t 2-4t, 0 le t le 10 where t is measured in seconds. Assuming positive speed, what time does it reach it's maximum velocity? (a) 0 seconds (b) 0.5 seconds (c) 2 seconds (d) 10 seconds (e) Never

Explanation / Answer

v = Integral of a*dt To find the time at which v is maximum, differentiate v and equate it to 0. =>dv/dt = a = 0 =>t*e^(2t^2-4t) = 0 =>t = 0 or e^(2t^2-4t) = 0 But second one can never happen da/dt = e^(2t^2-4t) + t*e^(2t^2-4t)*(4t-4) at t = 0, da/dt = 1 + 0 = 1 > 0.......So at t = 0, v is minimum So it will never reach maximum speed or velocity......Option e

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