the driver of a truck comes suddenly upon a falen tree that has blocked the road

Question

the driver of a truck comes suddenly upon a falen 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 contant velocity)

Explanation / Answer

Given Total time interval , T = 5.45 s Reaction time, t1 = 1.25 s Time period when the brakes were engaged, t2 = 5.45 s -1.25 s = 4.2 s Deceleration of the truck, a = - 5.60 m/s^2 Distance travelled by the truck after brakes were applied is, s = 62.4 m -------------------------------------------------------------------------- We will calculate the speed of the truck at the time when it hit the tree s = vi t2 + 1/2 a t2^2 62.4 m = vi (4.2 s) + 1/2 (-5.60 m/s^2)(4.2 s)^2 vi = 26.6 m/s This is the constant velocity of the truck . Now, the distance travelled by the truck during the reaction time is d = vi * t1    = 26.6 m/s (1.25 s) d = 33.25 m

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