Question

at a speed of 60 mph (26.8 m/s). Suddenly, a deer jumps in the road causing Earl to slam on his brakes with a deceleration of -4.91 m/s2. If it takes Earl 2.0 seconds to react to the deer, and the deer is 140 meters from the front of the truck, how close does Earl come to hitting the deer and damaging his new truck?

Answer 1

Initial velocity of truck is, $u=26.8 m/s$

Retardation is, $a=-4.91m/s^2$

Reaction time is 2 seconds

Distance covered in reaction time is, $S_1=26.8*2=53.6m$

Time taken by truck to come to rest, $t=(v-u) /a=(0-26.8)/(-4.91)=5.5s$

Distance covered in 5.5 seconds is, $S_2=ut-\frac{1}{2}at^2=(26.8*5.5)-(4.91*5.5*5.5/2)=73.14m$

Total distance covered by truck is, $S=S_1+S_2=53.6+73.14=126.74m$

Then distance between truck and deer is $D=140-126.74=13.26m$