Suppose the velocity v of a motorboat coasting in water satisfies the differential equation dv/dt=kv2. The initial speed of the motorboat is v (0) = 10m/s and v is decreasing at a rate of 1 m/s^2 when v = 5 m/s. Required:
How long does it take for the velocity of the boat to decrease to 1 m/s^2 to 1/10 m/s^2, when does it come to a stop?

Answertraveling around a circular trackexplanation"traveling around a circular track" is the best answer as you could be traveling around a circular track at a constant speed. your velocity would therefore have the same magnitude but will always be constantly direction. since acceleration is the rate of change of velocity, the rate of change will only involve the direction of velocity and not the magnitude.wrong choices: "an object at rest" does not accelerate at all"increasing speed while traveling around a curve" means that the acceleration will not be constant due to only change in direction; it will be constant due to both magnitude and direction"an object in free fall" does not necessarily change direction