Mathematics

If s = (2 + 3t)(5t – 4), find ds/dt when t = 4/5 secs

If s = (2 + 3t)(5t – 4), find ds/dt when t = 4/5 secs

  • A.
    0 units per sec
  • B.
    15 units per sec
  • C.
    22 unit per sec
  • D.
    26 units per sec
Correct Answer: Option C
Explanation

x = (2+3t)(5t-4)
Let u = 2+3t ∴du/dt = 3
and v = 5t-4 ∴dv/dt = 5
dx/dt = Vdu/dt + Udv/dt
= (5t-4)3 + (2+3t)5
= 15t – 12 + 10 + 15t
= 30t – 2
= 30×4/5 – 2
= 24 – 2
= 22