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/
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.
To find the particle's velocity at t = 10 seconds, we need to find the derivative of the position function with respect to time.
Given: s = 6 + 3t^0.5
The derivative of s with respect to t is:
ds/dt = d/dt(6 + 3t^0.5)
= 0 + 3(0.5)t^(-0.5) (using the power rule for derivatives)
= 1.5t^(-0.5)
Now we can calculate the velocity at t = 10 seconds by plugging in t = 10 into the derivative:
v(10) = 1.5(10)^(-0.5)
= 1.5/√(10)
Therefore, the particle's velocity at t = 10 seconds is 1.5/√(10) ms.