Question

The displacement of a particle is $s=(a+bt{)}^6$, where $a$ and $b$ are constants. Find acceleration of the as a function of time.

• A. $30b^2(a+bt{)}^4$
• B. $30b^2(a+bt{)}^3$
• C. $6b(a+bt{)}^5$
• D. $30b^2(a+bt{)}^5$

Answer 1

Answer: (A)

$30b^2(a+bt{)}^4$

Given,

$s=(a+bt{)}^6$

Velocity, $v=\frac{ds}{dt}$

$v=\frac{d(a+bt{)}^6}{dt}$

$v=6b(a+bt{)}^5$

Acceleration $=\frac{dv}{dt}$

$=\frac{d\left[6b\right(a+bt{)}^5]}{dt}$

$=30b^2(a+bt{)}^4$

The correct option is A.