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. (1 point) Responses 1/12 ms 6 ms 2/23√ ms 1/4 ms 15 ms/

Answer 1

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

s = 6 + 3√t

Taking the derivative:

ds/dt = d/dt (6 + 3√t)
= 3/(2√t)

Now, we can plug in t = 10 seconds:

ds/dt = 3/(2√10)
= 3/(2√2√5)
= 3/(4√10)
= (3/4) * (1/√10) * √10/√10
= (3/4) * 1/√10 * √10/√10
= (3/4)(1)
= 3/4

Therefore, the velocity of the particle at t = 10 seconds is 3/4 m/s.