Question

The displacement of a particle moving along 𝑥-axis is given by $x=a+bt+c{t}^2$. The acceleration of the particle is

• A. $b+c$
• B. $2c$
• C. $b$
• D. $c$

Answer 1

The correct option is B $2c$

Find magnitude of velocity of the particle.

Formula used: $v=\frac{dx}{dt}$
Given, displacement of the particle,
$x=a+bt+c{t}^2$
So, magnitude of velocity of the particle,
$v=\frac{dx}{dt}$
$v=b+2tc$

Find magnitude of acceleration of the particle.

Formula used: $a=\frac{dv}{dt}$
Magnitude of acceleration of the particle, $a=\frac{dv}{dt}$
$a=2c$