Question

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

• A. Rotation
• B. Velocity
• C. Acceleration
• D. Retardation

Answer 1

The correct option is C

Acceleration

Step 1. Given data

A particle is moving along the curve $x=a{t}^2+bt+c$

$ac=b^2$

Step 2. Finding the acceleration

Velocity is the change in the position with respect to the time.

Acceleration is the change in the velocity with respect to the time.

$$\begin{gathered} x=a{t}^2+bt+c \\ v=\frac{dx}{dt} \\ v=2at+b \\ A=\frac{dv}{dt} \\ A=2a \end{gathered}$$ [ $v$ is velocity, $A$ is acceleration]

As the value of the acceleration is constant then the particle will move with the uniform acceleration.

Thus, the particle would be moving with uniform Acceleration.

Hence, option $\left(C\right)$ is correct.