Question

the friction of water on a boat produces an acceleration of -10m/s^2. if the boat is traveling at 30 m/s and the motor shut off, how long does it take the boat to slow down to 5.0 m/s?

Answer 1

Answer:

The boat takes 2.5 seconds to slow down to 5 m/s

Explanation:

Motion With Constant Acceleration

It's a type of motion in which the velocity of an object changes uniformly in time.  The equation that rules the change of velocities is:

$v_f=v_o+at\qquad\qquad [1]$

Where:

a   = acceleration

vo = initial speed

vf  = final speed

t    = time

Using the equation [1] we can solve for a:

$\displaystyle a=\frac{v_f-v_o}{t}$

The acceleration produced by the friction of water is $a=-10 \ m/s^2$ and the boat is initially traveling at v0=30 m/s. When the motor is shut off, the boat will start braking until it stops. We need to find the time it takes to ready the final speed of vf=5 m/s.

Let's solve the above equation for t:

$\displaystyle t=\frac{v_f-v_o}{a}$

$\displaystyle t=\frac{5-30}{-10}$

$\displaystyle t=\frac{-25}{-10}$

t = 2.5 s

The boat takes 2.5 seconds to slow down to 5 m/s