Question

1. a car is driving down a road in the early morning when a deer walks into the road. if the deer was 25 meters away when the driver noticed it and the car was traveling at 20 m/s, did the car strike the deer? assume instant - reaction time and that the car has a braking acceleration of - 6.53 m/s².

yes, the car struck the deer because the stopping distance exceeded the distance between the car and the deer.
no, the car did not strike the deer because the stopping distance was less than the distance between the car and the deer.
yes, the car struck the deer because the cars brakes did not decelerate the car at an acceptable rate.
no, the car did not strike the deer because the deceleration of the car was greater than that of the deer.

Explanation:

Step1: Identify the known - values

Initial velocity $u = 20\ m/s$, final velocity $v = 0\ m/s$, acceleration $a=- 6.33\ m/s^{2}$, and initial distance $d = 25\ m$.

Step2: Use the kinematic equation $v^{2}-u^{2}=2as$

We want to find the stopping - distance $s$. Rearranging the equation $v^{2}-u^{2}=2as$ for $s$, we get $s=\frac{v^{2}-u^{2}}{2a}$.
Substitute $v = 0$, $u = 20\ m/s$, and $a=-6.33\ m/s^{2}$ into the formula:
\[

$$\begin{align*} s&=\frac{0-(20)^{2}}{2\times(-6.33)}\\ &=\frac{- 400}{-12.66}\\ &\approx31.6\ m \end{align*}$$

\]

Step3: Compare the stopping - distance with the initial distance

The initial distance between the car and the deer is $d = 25\ m$, and the stopping - distance $s\approx31.6\ m$. Since $s>d$, the car struck the deer.

Answer:

Yes, the car struck the deer because the stopping distance exceeded the distance between the car and the deer.