Question

The relation between time and distance of a moving body is $t=5x^2+7x+8$. The acceleration of the body will be :

• A. $-10v^3$
• B. $-10v^2$
• C. $10v^3$
• D. $10v^2$

Answer 1

The correct option is A $-10v^3$

$\because$ Given $t=5x^2+7x+8$
$\therefore \frac{dt}{dx}=10x+7$
$\therefore \frac{dx}{dt}=v=\frac{1}{10x+7}$ $[\frac{dx}{dt}=v]...\left(i\right)$
$\because$ Acceleration , $a=\frac{dv}{dt}$
$=\frac{dv}{dx}\cdot \frac{dx}{dt}=v\cdot \frac{dv}{dx}$
$v\cdot \left[\frac{0-10}{(10x+7{)}^2}\right]$
$=-10v^3$ using Eqs. (i)