Answer to Question #112179 in Classical Mechanics for Kai Halcon

Question

As you’re driving home, you are nearing an intersection, traveling at a constant velocity of 11.11 m/s. a Ferrari is stopped at the red traffic light of the intersection. as you arrive towards the intersection, the traffic light becomes green with you 15 m away, and concurrently, the Ferrari accelerates from rest at 3 m/s^2 . you continue at constant speed. How far from the stop line do you pass the Ferrari? At what time, measured from when the light turned green, do you pass the Ferrari?

Answer 1

As per the given question,

traveling speed(v) =11.11m/sec

the distance between me and the traffic light when light became green=15m

acceleration of the ferrari$(a) = 3 m/sec^2$

Now, let at the time t, both will just cross to each other, let the distance travelled by me in t sec is

so $d=vt=11.11\times t------(i)$

Similarly,

$15-d= \dfrac{at^2}{2}=\dfrac{3\times t^2}{2}------(ii)$

Now, from equation (i) and (ii)

$15-11.11t=1.5t^2$

$\Rightarrow 1.5t^2+11.11t-15=0$

$t=\dfrac{-11.11\pm \sqrt{11.11^2+2\times 1.5\times 15}}{2\times 11.11}sec$

$\Rightarrow t=\dfrac{-11.11\pm 12.97}{22.22}$

Now, here we will consider positive value,

so, $t=\dfrac{-1.86}{22.22}=0.083sec$