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

Question

A particle is moving along the curve x = at2 + bt + c. If ac - b2, then particle would be moving with uniform (A) rotation (B) velocity (C) acceleration (D) retardation

Tardigrade Admin · Accepted Answer

Given curve is x = at2 + bt + c On differentiating w.r.t. t, we get (dx/dt) = 2at + b Again on differentiating, we get acceleration (d2x/dt2) = 2a ∴ Particle is moving with uniform acceleration.

Q. A particle is moving along the curve $x = a t^{2} + b t + c$ . If $a c - b^{2}$ , then particle would be moving with uniform

rotation

velocity

acceleration

retardation

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

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