Question
The position of a particle at time t is given by s. Find the velocity ds/dt.
S^4-6st+3t^5-5t=0
S^4-6st+3t^5-5t=0
Answers
GPT 3.5
To find the velocity of the particle, we need to find the derivative of the position function s with respect to time t, which is denoted as ds/dt.
Given the position function:
s(t) = t^4 - 6st + 3t^5 - 5t
To find ds/dt, we need to differentiate s(t) with respect to t term by term:
ds/dt = d/dt(t^4) - 6s(d/dt(t)) + d/dt(3t^5) - d/dt(5t)
ds/dt = 4t^3 - 6s + 15t^4 - 5
Therefore, the velocity of the particle at time t is ds/dt = 4t^3 - 6s + 15t^4 - 5.
Given the position function:
s(t) = t^4 - 6st + 3t^5 - 5t
To find ds/dt, we need to differentiate s(t) with respect to t term by term:
ds/dt = d/dt(t^4) - 6s(d/dt(t)) + d/dt(3t^5) - d/dt(5t)
ds/dt = 4t^3 - 6s + 15t^4 - 5
Therefore, the velocity of the particle at time t is ds/dt = 4t^3 - 6s + 15t^4 - 5.