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  4. A particle is moving along the curve x = at2 + bt + c. If ac - b2, then particle would be moving with uniform

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Q. A particle is moving along the curve $x = at^2 + bt + c$. If $ac - b^2$, then particle would be moving with uniform

Application of Derivatives

Solution:

Given curve is $x = at^2 + bt + c$
On differentiating w.r.t. $t$, we get
$\frac{dx}{dt} = 2at + b$
Again on differentiating, we get acceleration $\frac{d^{2}x}{dt^{2}} = 2a$
$\therefore $ Particle is moving with uniform acceleration.