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
Answers
GPT 3.5
To find the velocity, we need to differentiate the position function s with respect to time t.
Given s = s^4 - 6st + 3t^5 - 5t
ds/dt = d/dt (s^4) - d/dt (6st) + d/dt (3t^5) - d/dt (5t)
ds/dt = 4s^3 * ds/dt - 6s - 6t + 15t^4 - 5
Substitute s = s^4 - 6st + 3t^5 - 5t
ds/dt = 4(s^4 - 6st + 3t^5 - 5t)^3 - 6(s^4 - 6st + 3t^5 - 5t) - 6t + 15t^4 - 5
Given s = s^4 - 6st + 3t^5 - 5t
ds/dt = d/dt (s^4) - d/dt (6st) + d/dt (3t^5) - d/dt (5t)
ds/dt = 4s^3 * ds/dt - 6s - 6t + 15t^4 - 5
Substitute s = s^4 - 6st + 3t^5 - 5t
ds/dt = 4(s^4 - 6st + 3t^5 - 5t)^3 - 6(s^4 - 6st + 3t^5 - 5t) - 6t + 15t^4 - 5