2025 TKSS PRELIMS P2 Q7

An object starts from rest from a point \(O\).

Its velocity, \(v\) cm/s, \(t\) seconds after leaving \(O\), is such that \(\frac{dv}{dt}=10\).

After 5 seconds, the object reaches a point \(A\).

1. Find its velocity at \(A\).[2]
2. Find the distance \(OA\).[2]

On reaching \(A\), the object enters a second stage of motion in which its velocity \(V\) cm/s, \(T\) seconds after leaving \(A\), is such that \(\frac{dV}{dT}=10-k\sqrt{T}\), where \(k\) is a constant.

3. Given that the object’s velocity at a point \(B\) where \(T=4\) is 26 cm/s, show that \(k=12\).[3]