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An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < -6 N , 2 N># and the second is #F_2 = < 6 N, 3 N>#. What is the object's rate and direction of acceleration?

Answer 1

Amelia Adams

The rate of acceleration is #=2.5ms^-2# in the direction of #=90º#

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-6,2>+<6,3>#

#=<0,5>#

We apply Newton's second Law

#vecF=m veca#

Mass, #m=2kg#

#veca =1/m*vecF#

#=1/2<0,5> = <0, 5/2>#

The magnitude of the acceleration is

#||veca||=||<0,5/2>||#

#=sqrt((0)^2+(5/2)^2)#

#=sqrt(25)/2=2.5ms^-2#

The direction is #theta = arctan((5)/(0))#

The angle is in the 1st quadrant

#theta=arctan(5/0)=90#º

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Answer 2

Julia Aguilar

The object's acceleration is \( a = < 0 \, \text{m/s}^2, 1 \, \text{m/s}^2 > \).

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Answer from HIX Tutor

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.

An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= &lt; -6 N , 2 N&gt;# and the second is #F_2 = &lt; 6 N, 3 N&gt;#. What is the object's rate and direction of acceleration?

An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < -6 N , 2 N># and the second is #F_2 = < 6 N, 3 N>#. What is the object's rate and direction of acceleration?