Find initial position via intergration???

An object moves in a straight line with an acceleration of 8m/s^2. If after 1 second it passes through point O and after 3 seconds it is 30 meters from O, find its initial position relative to O.

1 Answer
Jim H
May 7, 2018

Without knowing whether the position at 3 seconds is 30 meters left or right of O (or knowing whether the initial velocity is positive or negative) there are two correct answers.

Explanation:

a=8

Using v0 for the initial velocity,

v(t)=8t+v0

Using s0 for the initial position.

s(t)=4t2+v0t+s0

We have been asked to find s0 as a function of O (the position at time 1 second.).

Using the values given for t=1 and t=3, we get

s(1)=4+v0+s0=O and

s(3)=36+3v0+s0=O±30

Subtracting the first equation from the second yields:

32+2v0=±30 So

2v0=−2 or −62

So v=−1 or v=−31.

This gives us:
Solution 1

s(t)=4t2−t+s0 and, again using the information at t=1, we find

s(1)=4−1+s0=O,

so s0=O−3

Solution 2

s(t)=4t2−3t+s0 and, again using the information at t=1, we find

s(1)=4−31+s0=O,

so s0=O−27

Related questions
Impact of this question
1221 views around the world
You can reuse this answer
Creative Commons License