Question

the position of a particle moving along a coordinate line is s=6+3t−−−−−√ , with s in meters and t in seconds. Find the particle’s velocity at t = 10 seconds.

Answer 1

To find the velocity of the particle, we need to take the derivative of the position function with respect to time.

Given: s = 6 + 3√t

Taking the derivative of the position function, we get:

v = d/dt (6 + 3√t)

To find the derivative of √t, we can use the chain rule, which states that for a function f(g(t)), the derivative is given by f'(g(t)) * g'(t).

In this case, f(u) = √u, and g(t) = t. So, the derivative of √t is given by:

d/dt (√t) = (1/2√t) * (1) = 1/(2√t)

Substituting this in the velocity equation, we get:

v = d/dt (6 + 3√t)
= 0 + 3 * (1/(2√t))
= 3/(2√t)

Now we can find the particle's velocity at t = 10 seconds:

v(10) = 3/(2√10)
= (3/2) √10

Therefore, the particle's velocity at t = 10 seconds is (3/2) √10 m/s.