Question

The particle's position as a function of time is given as $x=5t^2-9t+3$. Find out the maximum value of position co-ordinate?

Answer 1

We are given $x=5t^2-9t+3$, the position is changing with $x$.
Differentiate $x$ w.r.t. $t$, we get $\frac{dx}{dt}=10t-9=0$
$\therefore t=9/10=0.9$
Check whether maxima or minima exists.
We need to do double differentiation test : $\frac{d^{2}x}{d{t}^2}=10>0$
Therefore, there exists a minima at $t=0.9$
Now, check for the limiting values.
When $t=0,x=3$ and when $t=\infty ,x=\infty$.
So, the maximum position co-ordinate does not exist.