# Physics question

#### bigbutrealdreams

2+ Year Member
For the case of 1-dimensional constant acceleration, write an expression for position, s, as a function of time, t. Would this expression still hold true for acceleration which changes as a function of time?

#### BluMist

##### I'm the only one of me. Baby, that's the fun of me
Gold Donor
2+ Year Member
not exactly sure what you asking, but taking a stab at it, seems to be more of a calculus question than physics

if a = a0 (constant)
velocity = integral of a = a0 * t + v0 (constant)
distance = integral of v = 1/2 a0 * t^2 + v0 * t + s0 (constant) - this should seem familiar to you as the standard equation

if a is a function of time, let's say a = a0 * t - acceleration increases linearly with time
velocity = integral of a = 1/2 a0 * t^2 + v0 - if acceleration is linear, then velocity is ^2
distance = integral of v = 1/6 a0 * t^3 + v0 * t + s0 - if velocity is ^2, then distance is ^3

so no, the expression is different as you integrate a as various functions of t