An object is at rest at #(1 ,9 ,1 )# and constantly accelerates at a rate of #1/3 m/s# as it moves to point B. If point B is at #(4 ,4 ,5 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

1 Answer
Jul 2, 2017

Answer:

#t = 6.51# #"s"#

Explanation:

We're asked to find the time #t# it takes an object to cover a distance with a given acceleration.

To do this, we can use the equation

#Deltax = v_(0x)t + 1/2a_xt^2#

We know it starts from a state of rest, so the initial velocity #v_(0x)# is zero, so our equation now becomes

#Deltax = 1/2a_xt^2#

To find the displacement #Deltax#, we need to find the distance between the two coordinate points, which is done by the distance formula:

#Deltax = sqrt((1-4)^2 + (9-4)^2 + (1-5)^2) = color(red)(7.07# #color(red)("m"#

And our acceleration is given as #1/3# #"m/s"^2#

Plugging in known values and solving for #t#, we have

#t = sqrt((2Deltax)/(a_x)) = sqrt((2(color(red)(7.07)color(white)(l)color(red)("m")))/(1/3color(white)(l)"m/s"^2)) = color(blue)(6.51# #color(blue)("s"#