Question

A particle moves on a coordinate line with acceleration Star tFraction d squared s Over dt squared End Fraction equals 60 Start Root t End Root minus Start Fraction 21 Over Start Root t End Root End Fraction ​, subject to the conditions that Start Fraction ds Over dt End Fraction equals 8 and sequals16 when t equals 1. Find
A) the velocity v equals Start Fraction ds Over dt EndFraction in terms of t
B) the position s in terms of t.

Answer 1

Answer:

Velocity , v (t) =  90√t³ -   42√t

Position , s (t) = 36 √t⁵ - 28√t³

Step-by-step explanation:

d²s/dt =60√t -21/√t,-------------------------------------------- (1)

Subject to:

ds/dt =8; 16 at t=1

Integrating equation (1) we have :

ds/dt = 90√t³ -   42√t-------------------------------------------------- (2)

s = ∫90√t³ -   42√t dt

 =      36 √t⁵ - 28√t³ --------------------------------------------------- (3)

Velocity , v (t) =  90√t³ -   42√t

Position , s (t) = 36 √t⁵ - 28√t³