##### Question

# A motorboat cuts its engine when its speed is 10.2 m/s and coasts to rest.

A motorboat cuts its engine when its speed is 10.2 m/s and coasts to rest. The equation describing the motion of the motorboatduring this period is *v* =*v*_{i}*e*^{–ct}, where *v* is the speed attime *t*, *v*_{i} is the initial speed, and *c* is a constant. At *t* = 20.5 s, the speed is 5.00 m/s.

(a) Find the constant *c*.

s^{-1}

(b) What is the speed at *t* = 40.0 s?

m/s

(c) Differentiate the expression for *v*(*t*) and thus show that the acceleration of the boat is proportional to the speed at any time.*ce ^{-ct}*

*cv*

_{i}

*-cv*

*cv*

_{i}

*e*

^{-ct}*-ce*

^{-ct}*cv*

## Solutions

##### Expert Solution

No answers