# Thread: Basic integration kinematics question

1. ## Basic integration kinematics question

Can someone please show me how to do this question?
I know you have to antidifferentiate twice to get the displacement function but am i not sure exactly what to integrate.

A body moves in a straight line with an acceleration of $10 m/s^2$
If after 2 seconds it passes through O and after 3 seconds is 25 metres from O, find its initial displacement relative to O.

Do I start off with $a=10t$ ?

Thanks, help is appreciated

2. Originally Posted by user_5
Can someone please show me how to do this question?
I know you have to antidifferentiate twice to get the displacement function but am i not sure exactly what to integrate.

A body moves in a straight line with an acceleration of $10 m/s^2$
If after 2 seconds it passes through O and after 3 seconds is 25 metres from O, find its initial displacement relative to O.

Do I start off with $a=10t$ ?

Thanks, help is appreciated
$a = 10 \Rightarrow \frac{dv}{dt} = 10 \Rightarrow v = 10t + C$.

$v = 10t + C \Rightarrow \frac{dx}{dt} = 10 t + C \Rightarrow x = 5 t^2 + Ct + K$.

Substitute $x(2) = 0$: $0 = 20 + 2C + K$ .... (1)

Substitute $x(3) = 25$: $25 = 45 + 3C + K$ .... (2)

Solve equations (1) and (2) simultaneously for C and K. Substitute the values for C and K into $x = 5 t^2 + Ct + K$.

To get initial displacement, substitute t = 0.