5. A particle starts from rest and moves in a straight line with an acceleration (𝑔 − 𝑘𝑣^2), where 𝑣 is its speed at any time 𝑡 and 𝑔 and 𝑘 are constants. Show that 𝑣^2 = 𝑔(1 − 𝑒^(-2𝑘𝑠))/𝑘, where 𝑠 is the distance travelled in time 𝑡. If the speed increases from 𝑉 to 5/4 𝑉 as 𝑠 increases from 𝑑 to 2𝑑, find an expression for 𝑘 in terms of 𝑉 and 𝑔.