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Mechanics

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Examples
and Solutions
 Linear Motion: A car travels at a uniform velocity of 20 m/s for 5s. The brakes are then applied and the car comes to rest with uniform retardation in a further 8s. How far does the car travel after the brakes are applied? Initial Velocity = u = 20 m/s Time traveled after brakes = t = 8s Distance traveled after brakes = s   Applying  v = u + at  (where a is the retardation)                       0 = 20 + 8a                      8a = -20                        a = -20/8                           = -2.5 m/s2 (note the minus sign for retardation)       Applying   s = ut + ½at2  (for the distance traveled after braking)                       s = (20)(8) + ½(-2.5)(8)2                             = 160 - (64)(5)/4                               = 160 - 80                                 = 80 m Linear Motion: A motorist, traveling at 90 km/h, applies his brakes and comes to rest with uniform retardation in 20s. Calculate the retardation in m/s2.      Initial Velocity = u = 90 km/h = (90 X 1000)/3600 m/s = 25                  Final Velocity = v = 0                     Time taken = t = 20s                       Retardation = a                           Applying   v = u + at                                         0 = 25 + 20a                                    - 20a = 25                                          a = -25/20                                             = -1.25 m/s2

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