If the initial position and initial velocity of a vehicle are known and a record is kept of the acceleration?

Question

at each instant, can you compute the vehicle's position after a certain time from these data? If so, explain how this might be done.

Answer 1

It's called 'inertial navigation' (or INAV) and it's been in use for 20+ years. The biggest problem with INAV systems is that the inertial sensors aren't too terrible accurate (especially at small values of acceleration) and the systems tend to 'drift'. Most INAV's have to be recalibrated at known 'fix' points every few hours.
These days, GPS is the -only- way to go ☺

Doug

Answer 2

They use the position/time equation:

position = (starting positing) + (strating speed)(time)
+(1/2)(Acceleration)(t^2)

or in math terms:

X = Xo + VoT + 1/2AT^2

V = AT

just carry out these calculations, and then update it, so that x becomes Xo, and V becomes Vo, and carry it out again (reitterate it).

do these calculations at a rate of about 1000 times a second.

it will drift because of rounding, the memory can only keep track of so many decimal places, when almost all decimal numbers are infinite and non-repeting.