# 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 $\displaystyle 10 m/s^2$
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 $\displaystyle a=10t$ ?

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 $\displaystyle 10 m/s^2$
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 $\displaystyle a=10t$ ?

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

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

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

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

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

To get initial displacement, substitute t = 0.