Question

The ponition of a particle moving along a coerdinale line is s= √28+6t, with s in meters and t in seconds. Find the rate of change of the particle's poaition at t=5 sec.

Answer 1

The rate of change of the particle's position at t = 5 sec is approximately 0.333 m/s.

Step-by-step explanation:

To find the rate of change of the particle's position at t = 5 sec, we need to find the derivative of the position equation with respect to t. The given equation is s = √(28 + 6t). We can rewrite it as s = (28 + 6t)^(1/2). Now, let's find the derivative:

Using the Chain Rule, we have:

ds/dt = (1/2)(28 + 6t)^(-1/2)(6)

Substituting t = 5 into the derivative equation:

s'(5) = (1/2)(28 + 6(5))^(-1/2)(6)

Simplifying further:

s'(5) = (1/2)(58)^(-1/2)(6)

Calculating the value:

s'(5) ≈ 0.333 m/s

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