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An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < 4 N , 1 N># and the second is #F_2 = < 5 N, 9 N>#. What is the object's rate and direction of acceleration?

Answer 1

Lily Adams

The rate of acceleration #=4.48ms^-2# in the direction #48.0#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <4,1>+<5,9>#

#=<9,10>#

we use Newton's second Law

#vecF=m veca#

#veca =1/m*vecF#

#=1/3<9,10> = <3, 10/3>#

The magnitude of the acceleration is

#||veca||=||<3,10/3>||#

#=sqrt((3)^2+(10/3)^2)#

#=sqrt(9+100/9)#

#=sqrt 181/3=4.48ms^-2#

The direction is #theta = arctan((10/3)/(3))#

The angle is in the 1st quadrant

#theta=arctan(10/9)=48.0#º

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Answer 2

Charles Aeschliman

The object's rate of acceleration is approximately 2.8 m/s² and its direction of acceleration is approximately 64 degrees above the horizontal axis.

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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 #3 kg# is acted on by two forces. The first is #F_1= &lt; 4 N , 1 N&gt;# and the second is #F_2 = &lt; 5 N, 9 N&gt;#. What is the object's rate and direction of acceleration?

An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < 4 N , 1 N># and the second is #F_2 = < 5 N, 9 N>#. What is the object's rate and direction of acceleration?