An object is at rest at (7 ,3 ,9 ) and constantly accelerates at a rate of 7/4 ms^-2 as it moves to point B. If point B is at (2 ,5 ,8 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

1 Answer
Jan 23, 2018

First we find the distance between the points, which is 5.5 m, then calculate the time taken, which is 2.5 s.

Explanation:

Find the distance between the points:

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

s=sqrt((7-2)^2+(5-3)^2+(9-8)^2)

s=sqrt(5^2+2^2+1^2)=sqrt(30)=5.5 m

Now to find the time taken:

s=ut+1/2at^2

The initial velocity, u, is just equal to 0 because the object is initially at rest, so this reduces to:

s=1/2at^2

t=sqrt((2s)/a)=sqrt((2xx5.5)/(7/4))=2.5 s