Question

Displacement of ab object is proportional to t^4 show that the acceleration is increasing with time

Answer 1

$\sf\underline\red{Solution:}$

• Displacement s = t³ Or
• s = kt³

$\green{\boxed{\bold a = \frac{dv}{dt} }} \\ \\ \green{\boxed{\bold v = \frac{ds}{dt} }}$

$\sf\underline\pink{If\:You\: Know\:basic\: Differentiation}$

$\longrightarrow\sf\orange{\boxed{v = Ds/dt = d(kt^3)/dt}} \\ \\ \longrightarrow\sf\orange{v = 3 \times k \times t^2} \\ \\ \longrightarrow\sf\orange{v = 3kt^2}$

Now Acceleration = a = dv/dt

$\implies\sf{a = d(3kt^2)/dt} \\ \\ \implies\sf{a = 3k \times 2t} \\ \\ \implies\sf{a = 6kt}$

Hope it will be helpful ✌️