Force and motion in Newton's laws

In summary, the boat's speed is initially 90 km/h and is slowed down by a frictional force proportional to its speed with a constant of 70. Using Newton's law 2, the time required for the boat to slow to 45 km/h is found by using the equation t = -m(V - Vi) / 70Vi (h), where m is the mass of the boat and Vi is the initial velocity. However, this solution is incorrect as acceleration is not constant in this scenario and cannot be solved using only one equation.
  • #1
theunloved
43
1
A 1000kg boat is traveling at 90 km/h when its engine is shut off. The magnitude of the frictional force fk between boat and water is proportional to the speed V of the boat: fk = 70V where V is in meters per second and fk is in Newtons. Find the time required for the boat to slow to 45 km/h.

Attempted to solve:
Take upwards as positive for y direction, x + from left to right

From Newton's law 2, we have:
-fk = ma
a = -fk/m = -70Vi / m

(Vi = V initial)

V = Vi + at
---------> t = (V - Vi) /a

t = - m(V - Vi) / 70Vi (h)
with m = 1000kg, V = 45km/h, Vi = 90 km/h

However, my answer is not correct from the book. Can someone point out where I did wrong ? Thanks
 
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  • #2
If the acceleration is based on the object's speed is it really constant?
 
  • #3
DukeLuke said:
If the acceleration is based on the object's speed is it really constant?

Oh I got it, since acceleration is not constant, we can't use all the kinematic equations to solve this problem...But how are we going to find acceleration if we only have one equation ?
 

1. What are Newton's laws of motion?

Newton's laws of motion are three fundamental principles that describe the relationship between force and motion. The first law states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by a net force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

2. What is the difference between mass and weight?

Mass is the amount of matter in an object and is measured in kilograms. Weight is the force of gravity acting on an object and is measured in Newtons. Mass is constant, but weight can change depending on the gravitational pull of the object's surroundings.

3. How does force affect motion according to Newton's second law?

According to Newton's second law, the acceleration of an object is directly proportional to the net force acting on it. This means that the greater the force applied, the greater the acceleration will be. Additionally, the acceleration is inversely proportional to the mass of the object, meaning that the more massive an object is, the less it will accelerate under the same force.

4. Can an object be in motion without a force acting on it?

According to Newton's first law, an object in motion will remain in motion at a constant velocity unless acted upon by a net force. This means that in the absence of a net force, an object will continue to move with the same speed and direction. However, it is important to note that some forces, such as friction, may act on an object to eventually slow it down and bring it to a stop.

5. How do Newton's laws apply to real-life situations?

Newton's laws of motion apply to a wide range of real-life situations, from the motion of objects on Earth to the movement of planets in space. These laws are used to explain and predict the behavior of objects in motion and are the basis for many technological advancements, such as airplanes and cars. They are also essential in fields such as engineering and physics, where understanding and applying these laws is crucial in designing and building structures and machines.

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