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An object is at rest at #(8 ,2 ,9 )# and constantly accelerates at a rate of #3 m/s# as it moves to point B. If point B is at #(6 ,7 ,3 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Answer 1

Emily Abbate

The time is #=2.32s#

The following equation of motion will be used:

#s=u_0t+1/2at^2#

#u_0=0#

Thus,

#s=1/2at^2#

#a=3ms^-2#

The distance between 2 points #A=(x_1,y_1,z_1)# and #B=(x_2.y_2.z_2)# is

#=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#

In this case,

#A=(8,2,9)# and #B=(6,7,3)#

Thus,

#s=sqrt((6-8)^2+(7-2)^2+(3-9)^2)#

#=sqrt(4+25+36)#

#=sqrt65#

Utilizing the motion equation,

#t^2=(2s)/a#

#t^2=(2*sqrt65)/(3)=5.37#

#t=sqrt5.37=2.32s#

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Answer 2

Adam Arnold

Using the kinematic equation ( s = ut + \frac{1}{2}at^2 ), where ( s ) is the displacement, ( u ) is the initial velocity, ( a ) is the acceleration, and ( t ) is the time, the time it takes for the object to reach point B is approximately 1.732 seconds.

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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.