An object with a mass of #9 kg# is acted on by two forces. The first is #F_1= < -2 N , -1 N># and the second is #F_2 = < 8 N, -5 N>#. What is the object's rate and direction of acceleration?
The object is accelerating at a rate of
at an angle of
The total force acting upon an object is the sum of all the forces acting on that object.
In this case
Then adding algebraically we get
and by Newton's 2nd Law
Then
The rate of acceleration is the magnitude of a.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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- If an object is moving at #14 m/s# over a surface with a kinetic friction coefficient of #u_k=10 /g#, how far will the object continue to move?
- An object with a mass of #4 kg# is on a plane with an incline of # - pi/4 #. If it takes #7 N# to start pushing the object down the plane and #5 N# to keep pushing it, what are the coefficients of static and kinetic friction?
- An object with a mass of #7 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 3+sin(4x) #. How much work would it take to move the object over #x in [pi, 4pi], where x is in meters?
- An object with a mass of #2 kg# is on a surface with a kinetic friction coefficient of # 3 #. How much force is necessary to accelerate the object horizontally at #6 m/s^2#?

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