Two cars are traveling along a straight-line in the same direction,the lead car

Question

Two cars are traveling along a straight-line in the same direction,the lead car at 25.0 m/s and the other car at 33.0 m/s. At the moment the cars are 40.0 m apart,the lead driver applies the brakes, causing his car to have anacceleration of -2.20 m/s2. (a) How long does it take for the lead car tostop?
s
(b) Assuming that the chasing car brakes at the same time as thelead car, what must be the chasing car's minimum negativeacceleration so as not to hit the lead car?
m/s2
(c) How long does it take for the chasing car to stop?
s (a) How long does it take for the lead car tostop?
s
(b) Assuming that the chasing car brakes at the same time as thelead car, what must be the chasing car's minimum negativeacceleration so as not to hit the lead car?
m/s2
(c) How long does it take for the chasing car to stop?
s

Explanation / Answer

        (a) Let initial velocity of lead car, u =   25.0m/s                           Finalvelocity of lead car, v kinematics=    0m/s                      accelerationof lead car, a  = -2.20m/s2.                      weknow that,                                              v= u + a t                                              0= 25.0 m/s   + (-2.20m/s2. ) t                                              2.2t = 25                                                    t= 25 / 2.2                                                      = 11.36 s       (b) distancetravelled by lead car before it stops, s = ut + 1/2at2                                                                                     =(25.0 m/s )(11.36 s) + 1/2 (-2.20m/s2. )(11.36 s)2                                                                                      =284 - 141.95                                                                                       =142.04 m             totaldistance to be travelled by the other car just to not hit the leadcar = 40 + 142.04                                                                                                                         =182.04 m             minimum acceleration required by the other car, a =(v 2 - u 2 ) /2s                                                                                          =(0 - 332) / (2) (182.04 )                                                                                           =- 2.99 m/s2.          (c) time required by chasing car to stop, t = (v - u) / a                                                                           =(0 - 33) / -2.99                                                                            =11 s                                                                                      =284 - 141.95                                                                                       =142.04 m             totaldistance to be travelled by the other car just to not hit the leadcar = 40 + 142.04                                                                                                                         =182.04 m             minimum acceleration required by the other car, a =(v 2 - u 2 ) /2s                                                                                          =(0 - 332) / (2) (182.04 )                                                                                           =- 2.99 m/s2.          (c) time required by chasing car to stop, t = (v - u) / a                                                                           =(0 - 33) / -2.99                                                                            =11 s

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