Question

A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates (meters) of the rabbit's position as function of time t(seconds) are given by

$x\left(t\right)=-\frac{t^2}{2}+5t+20$
And $y\left(t\right)=t^2-10t+30$

Find the velocity at time t = 15s.

• A. $20\hat{i}+40\hat{j}$
• B. $20\hat{i}+20\hat{j}$
• C. $-10\hat{i}+20\hat{j}$
• D. $-10\hat{i}+40\hat{j}$

Answer 1

The correct option is C

$-10\hat{i}+20\hat{j}$

$x=-\frac{t^2}{2}+5t+20,y=t^2-10t+30$
Let the x component of velocity be $v_x$ and y component $v_y$
$\therefore v_x=\frac{dx}{dt}=-\frac{2t}{2}+5=-t+5$
$v_y=\frac{dy}{dt}=2t-10$
At t= 15s
$v_x=-15+5=-10,v_y=2\left(15\right)-10=20$.
$\therefore \overrightarrow{v}=-10\hat{i}+20\hat{j}$