A motorboat starts from rest (initial velocity v(0)=v0=0 ft/s. Its motor provides a constant acceleration of 4 ft/s2 but water resistance causes a deceleration of v2400 ft/s2. a) Write the differential equation for the velocity v. b) Find v when t=10s c) Find the limiting velocity as t→[infinity] (that is, the maximum possible speed of the boat.)

The correct question is:

A motorboat starts from rest (initial velocity v(0) = v_0 = 0). Its motor provides a constant acceleration of 4 ft/s², but water resistance causes a deceleration of v²/400 ft/s².

(a) Write a differential equation for the velocity v.

(b) Find v when t = 10s, and also find the limiting velocity as t → ∞ (that is, the maximum possible speed of the boat).

(a) The differential equation is:

dv/dt = 4 - (v²/400)

(b) v = 30.46ft/s when t = 10s.

(c) The limiting velocity as t → ∞ is 40ft/s

Step-by-step explanation:

(a) The differential equation is formed by considering the changes in acceleration. At a constant acceleration of 4 ft/s², it then decelerate at v²/400 ft/s².

Adding these, we have

Acceleration, a = 4 - (v²/400)

Because acceleration is the derivative of velocity, a = dv/dt.

dv/dt = 4 - (v²/400)

(b) The differential equation obtained in (a) is solved, and evaluated at t = 10, to obtain v = 30.46 ft/s

(c) The limiting velocity, taking into consideration the properties of limit is evaluated to obtain v = 40 ft/s.

SEE ATTACHMENT FOR THE STEP BY STEP WORKINGS.

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol