K.E. = αs2
or, 1/2 mv2 = αs2
⇒ v2 = {2α s2}/{m} ...(i)
Differentiating both side w.r.t. 't' we have
⇒ dv/dt = {2αs}/{m} = aT (Tangential component of acceleration)
Now centripetal acceleration is
ac = v2/R = {2αs2}/{mR} [using equation (i)]
Net acceleration of the particle is given by
Now, force acting on the particle is given by,
F = ma = m x {2αs}/{m} √{1 + (s2/R2)}
= 2 α s√{1 + s2/R2}