Question

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$\text sf the displacement of body varies with time s=2+3t^{2}. find velocity at t=2 sec$

answer is : 12m/s

Answer 1

Answer:

Question: Displacement of body varies with time as 2 + 3t². We are required to find the velocity of the body at Time = 2 seconds.

We know that,

Velocity in Differentials can be written as:

v = dx / dt

Here, x = 2 + 3t²

So, dx / dt = d ( 3t² + 2 ) / dt

⇒ dx / dt = 2. 3t²⁻¹ = 2.3t = 6t

Hence v = 6t

Now we are required to find the velocity at 2 seconds. Hence substituting the value of t = 2, we get,

⇒ v = 6t = 6 × 2 = 12 units per second

Hence Velocity is 12 units per second