Car A, driving at 30.0 meters/second, enters a one lanetunnel. The driver observ

Question

Car A, driving at 30.0 meters/second, enters a one lanetunnel. The driver observes car B at 155 meters ahead traveling at5 meters/second. Car A applies the brakes but can only accelerateat -2.00 meters/second2 due to the road being wet. Willthere be a collision? if so, determine how far into the tunnel andat what time the collision occurs. If not, determine the distanceof the closest approach between Car A and car B. I used the following: Xf = final displacement Xi = initial displacement Vix = initial velocity T = time A = acceleration I made two equations for car A and B, and then I set themequal to each other to find T. Because I found a value for T, doesthat mean car A hit car B?

Explanation / Answer

1) Ans say distance travel by car A s1=ut+1/2 at2                                             s1=30t-t2    (accleration is negative   ; u is intial speed) say distance travel by car B s2=5t (constant speed so noacceleration a=0) if there is collision between cars this implies distances1=155+s2    (distance should be same) 30t-t2 =155+5t t2-25t+155=0 this is quadratic equation roots are=   (25+(625-620))/2 and (25-(625-620))/2 these values are positive that means collision occurs if time comes out to be negative collision doesnt occur becausetime is negative distance=155+5*t this is from car A ( use small time ) distance=5*t this is from car B

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