Use vocabulary from Newton’s 2nd law (acceleration and mass) to explain using one sentence in your own words, which one of the vehicles that are traveling at the same rate of speed will reach their destination first:
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Explanation:
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Newton's laws of motion
What is Newton's second law?
Learn about the fact that forces cause acceleration.
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What is Newton's second Law?
In the world of introductory physics, Newton's second law is one of the most important laws you'll learn. It's used in almost every chapter of every physics textbook, so it's important to master this law as soon as possible.
We know objects can only accelerate if there are forces on the object. Newton's second law tells us exactly how much an object will accelerate for a given net force.
\Large a=\dfrac{\Sigma F}{m}a=
m
ΣF
a, equals, start fraction, \Sigma, F, divided by, m, end fraction
To be clear, aaa is the acceleration of the object, \Sigma FΣF\Sigma, F is the net force on the object, and mmm is the mass of the object.
Wait, I thought Newton's second law was F=ma?
Looking at the form of Newton's second law shown above, we see that the acceleration is proportional to the net force, \Sigma FΣF\Sigma, F, and is inversely proportional to the mass, mmm. In other words, if the net force were doubled, the acceleration of the object would be twice as large. Similarly, if the mass of the object were doubled, its acceleration would be half as large.
What does net force mean?
A force is a push or a pull, and the net force \Sigma FΣF\Sigma, F is the total force—or sum of the forces—exerted on an object. Adding vectors is a little different from adding regular numbers. When adding vectors, we must take their direction into account. The net force is the vector sum of all the forces exerted on an object. What does the term vector sum mean?
For instance, consider the two forces of magnitude 30 N and 20 N that are exerted to the right and left respectively on the sheep shown above. If we assume rightward is the positive direction, the net force on the sheep can be found by
\Sigma F = 30\text{ N} - 20\text{ N}ΣF=30 N−20 N\Sigma, F, equals, 30, start text, space, N, end text, minus, 20, start text, space, N, end text
\Sigma F = 10\text{ N to the right}ΣF=10 N to the right\Sigma, F, equals, 10, start text, space, N, space, t, o, space, t, h, e, space, r, i, g, h, t, end text
If there were more horizontal forces, we could find the net force by adding up all the forces to the right and subtracting all the forces to the left.
Since force is a vector, we can write Newton's second law as \vec a=\dfrac{\Sigma \vec F}{m}
a
=
m
Σ
F
a, with, vector, on top, equals, start fraction, \Sigma, F, with, vector, on top, divided by, m, end fraction. This shows that the direction of the total acceleration vector points in the same direction as the net force vector. In other words, if the net force \Sigma FΣF\Sigma, F points right, the acceleration aaa must point right.
How do we use Newton's second law?
If the problem you're analyzing has many forces in many directions, it's often easier to analyze each direction independently.
In other words, for the horizontal direction we can write
\Large a_x=\dfrac{\Sigma F_x}{m}a
x
=
m
ΣF
x
a, start subscript, x, end subscript, equals, start fraction, \Sigma, F, start subscript, x, end subscript, divided by, m, end fraction
This shows that the acceleration a_xa
x
a, start subscript, x, end subscript in the horizontal direction is equal to the net force in the horizontal direction, \Sigma F_xΣF
x
\Sigma, F, start subscript, x, end subscript, divided by the mass.
Similarly, for the vertical direction we can write
\Large a_y=\dfrac{\Sigma F_y}{m}a
y
=
m
ΣF
y
a, start subscript, y, end subscript, equals, start fraction, \Sigma, F, start subscript, y, end subscript, divided by, m, end fraction
This shows that the acceleration a_ya
y
a, start subscript, y, end subscript in the vertical direction is equal to the net force in the vertical direction, \Sigma F_yΣF
y
\Sigma, F, start subscript, y, end subscript, divided by the mass.
When using these equations we must be careful to only plug horizontal forces into the horizontal form of Newton's second law and to plug vertical forces into the vertical form of Newton's second law. We do this because horizontal forces only affect the horizontal acceleration and vertical forces only affect the vertical acceleration. For instance, consider a hen of mass mmm that has forces of magnitude \redD{F_1}F
1
start color #e84d39, F, start subscript, 1, end subscript, end color #e84d39, \blueD{F_2}F
2
start color #11accd, F, start subscript, 2, end subscript, end color #11accd, \greenD {F_3}F
3
start color #1fab54, F, start subscript, 3, end subscript, end color #1fab54, and F_4F
4
F, start subscript, 4, end subscript exerted on it in the directions shown below.