Question

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$\sf \implies \: the displacement\: of \: body\: varies\: with\: time\: s\:=t^{3}\:+3t^{2}\:+2t\:-1.\:. if\: velocity\: at\: t\:=4sec\: is\: 2+2k \: m/s\: then\: find\: k$

answer : 6

Answer 1

Answer:

Displacement varies with time 't' = t³ + 3t² + 2t - 1

Correction: Velocity at 4 seconds = 2 + 12k m/s

We know that,

Velocity = dx / dt

⇒ dx / dt = d ( t³ + 3t² + 2t - 1 ) / dt = 3t² + 6t + 2

At time t = 4 seconds we get,

⇒ V = 3 ( 4 )² + 6 ( 4 ) + 2

⇒ V = 3 × 16 + 24 + 2 = 48 + 24 + 2 = 74 m/s

Now it is given that, V at 4 seconds is 2 + 12k m/s then,

⇒ 2 + 12k = 74

⇒ 12k = 74 - 2 = 72

⇒ 12k = 72

⇒ k = 72 / 12 = 6

Hence value of k is 6.