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The driver of a truck comes suddenly upon a fallen tree that has blocked the road ahead. A total time interval of 5.45 seconds elapses during which the driver recognizes the hazard, determines the need to brake, hits the pedal, and ultimately slams into the tree. The driver's reaction time uses the first 1.25 seconds of the total time. Once the brakes engage the truck experiences a constant 5.60 m/s^2 deceleration. The truck leaves skid marks on the road surface 62,4 m in length beginning where the brakes first engage and ends at tree. At what speed does truck hit tree and how far does the truck travel during the initial 1.25 second response interval (assume constant velocity)?

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Problem: The driver of a truck comes suddenly upon a fallen tree that has blocked the road ahead a total time interval of 5.45 seconds elapses during which the driver recognizes the hazard, determines the need to break, hits the pedal, and ultimately slams into the tree. The driver's reaction time uses the first 1.25 seconds of the total time. Once the brakes engage the truck experiences a constant 5.60 m/s^2 deceleration. The truck leaves skid marks on the road surface 62.4 m in length beginning where the brakes first engage and ends at tree. At what speed does truck hit tree and how far does the truck travel during the initial 1.25 second response interval (assume constant velocity).

Solution:
Total time interval = 5.45 sec
Driver^' s reaction time=1.25 sec
Time taken by the truck to slow down,t=(5.45-1.25)sec=4.2sec
Deceleration,a=5.6 m/s^2
Distance travelled,s=624m

Let the initial velocity be u.
s=ut-1/2 at^2
Or,624m=u*4.2s-1/2*5.6m/s^2*(4.2s)^2

Or,624m=u*4.2s-49.392m

Or,(624-49.392)m=u*4.2s

Or,574.608 m= u*4.2s

Or,u =(574.608 m)/4.2s=136.81 m/s

Final Velocity,v=u-at=136.81m/s-5.6 m/s^2×4.2s=113.29m/s

Thus, the speed with which the truck hits the tree is 113.29 m/s.
The initial speed of the truck is 136.81 m/s. Thus within the initial 1.25 second response interval, the truck travels a distance of s, given as:
s=ut=136.81m/s*1.25s=171.0125m

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