I am a little off on the following problem. the distance between car A and car B

Question

I am a little off on the following problem. the distance between car A and car B is 75 ft. Initialvelocity for a is 24mph, initial velocity for b is 36mph. Nowautomobiles A and B are traveling in adjacent highway lanes and att=0 have the positions and speeds indicated. Knowing thatautomobile A has a constant acceleration of 1.8 ft/s^2 and that Bhas constant deceleration of 1.2 ft/s^2, determine (a) when andwhere A overtake B, (b) the speed fo each automobile at thattime. I am a little off on the following problem. the distance between car A and car B is 75 ft. Initialvelocity for a is 24mph, initial velocity for b is 36mph. Nowautomobiles A and B are traveling in adjacent highway lanes and att=0 have the positions and speeds indicated. Knowing thatautomobile A has a constant acceleration of 1.8 ft/s^2 and that Bhas constant deceleration of 1.2 ft/s^2, determine (a) when andwhere A overtake B, (b) the speed fo each automobile at thattime.

Explanation / Answer

uA =24mph      =24*1.46     =35.04ft/sec uB = 36mph     = 36*1.46     =52.56ft/sec (a) let x is the distance at which A overtakes B and t is the time (ut+0.5at2)A=75+(ut+0.5at2)B 35.04t+0.5*1.8*t2 = 75+ 52.56t+0.5*1.2t2 =>0.3t2-17.52t-75=0 =>t= 62.4sec x = uAt+0.5aAt2 x = 35.04*62.4 + 0.5*1.8*62.42 x = 5690.88 ft (b) vA=uA+aAt => vA= 24+1.8*62.4 => vA=136.32 ft/sec or vA=93.3 mph vB=uB+aBt => vB= 36+1.2*62.4 => vB=110.88 ft/sec or vB=75.94mph

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