when driving at night at a speed of 80 km/hr, a deer suddenly appeared and frozen in your head light. The distance between your car and the deer was 45 meters at the moment you start to break your car as hard as possible in order to avoid the accident Assume that you could only generate a deceleration of -6m/s2 on your car, would both you and the deer be safe

100 km

v=80000/3600 = 22.2 m/s

the car decelerated at the distance
s1=v²/2•a=22.2²/2•6=41.15 m

41.15< 45 m
The driver and the deer will be safe

To determine whether both you and the deer would be safe, we need to calculate the distance it would take for your car to stop completely during your emergency braking.

First, let's find the initial velocity of your car in meters per second (m/s).
We know that the speed of your car is 80 km/hr, which can be converted to meters per second by multiplying it by 1000/3600 (to convert from km/hr to m/s).
So, the initial velocity of your car would be:
Initial velocity = 80 km/hr * (1000 m/1 km) * (1 hr/3600 s)

Second, let's calculate the time it takes for your car to stop. We know that the deceleration of your car is -6 m/s^2.
Using the equation of motion:
Final velocity = Initial velocity + (acceleration * time),
where the final velocity is 0 m/s (since the car stops), and the initial velocity is the value calculated in the first step.

Rearranging the equation: time = (Final velocity - Initial velocity) / acceleration.

Substituting the values, we have:
time = (0 m/s - initial velocity) / (-6 m/s^2)

Finally, we can calculate the distance traveled during this time using the equation:
Distance = Initial velocity * time + (0.5 * acceleration * time^2)

Now, let's plug in the values and calculate the distance:
Distance = initial velocity * time + 0.5 * acceleration * time^2

After calculating the distance, we'll compare it to the initial distance of 45 meters to determine if you can stop in time to avoid hitting the deer.

Once we have these calculations, we can determine if you would be able to stop before reaching the deer and if both you and the deer would be safe.