Question

at time a particle starts moving along the x-axis. if its kinetic energy increases uniformly with time ???t??? the net force acting on it must be proportional to:

Answer 1

It must be proportional to t

Answer 2

⭐hey there!!

Given that:

=> K ∝ t

Removing propornality sign we get,

➡ K = Ct

Where C is any arbitrary constant.

Now we know that K = ½ ×mv²

➡ ½ ×mv² = Ct

➡ mv² = 2Ct

➡ mv = √2Ct

➡ now we also know that : P = mv (momentum)

➡ P = √2ct

Here, We can see that, P ∝ √t

So Force(F) = dP/dt

➡ F ∝ t - ½

♦Hence Force is proportional to negative of half power of time. ✔
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Hope it will help u