Question

The displacement of particle is given by
$x=a_{0}+\frac{a_{1} t}{2}-\frac{a_{2} t^{2}}{3}$
What is its acceleration?

• A. $\frac{2 a_{2}}{3}$
• B. $-\frac{2 a_{2}}{3}$
• C. $ a_{2} $
• D. Zero

Answer 1

Answer: (B)

Acceleration is the rate of change of velocity and velocity is the rate of change of displacement.
The displacement equation is given by
$x=a_{0}+\frac{a_{1} t}{2}-\frac{\dot{a}_{2} t^{2}}{3}$
Velocity $=$ rate of change of displacement
i.e., $ v=\frac{d x}{d t}$
$=\frac{d}{d t}\left(a_{0}+\frac{a_{1} t}{2}-\frac{a_{2} t^{2}}{3}\right)$
$=0+\frac{a_{1}}{2}-\frac{2 a_{2} t}{3} $
$=\frac{a_{1}}{2}-\frac{2 a_{2} t}{3}$
Acceleration $=$ rate of change of velocity
i.e.,$a=\frac{d v}{d t}$
$=\frac{d}{d t}\left(\frac{a_{1}}{2}-\frac{2 a_{2}}{3} t\right)$
$=0-\frac{2 a_{2}}{3}$
$=-\frac{2 a_{2}}{3}$