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Suppose that barbara's velocity relative to alex is a constant v_(BA) = 52 km//h and car P is moving in the negative direction of the x axis (a) If alex measures a constant v_(PA) = -78 km//h for car P , what velocity v_(PB) will barbara measure ?(b) If car P brakes to a stop relative to alex (and thus relative to the ground ) in time t = 10 sat constant acceleration , what is its acceleration a_(PA) relative to alex?(c ) What is the acceleration a_(PB) of car P relative to barbara during the braking? |
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Answer» <P> Solution :We can attach a frame of reference A RO alex and a frame of reference B to barbara. Because the frames move at constant velocity relative to each other ALONG one axis , we can use`((v_(PA) = v_(PB) + v_(BA))` to relate `v_(PB)` to `v_(PA)` and `v_(BA)`(a)We find ` - 78 km//h = v_(PB) + 52 km//h` `v_(PB) = -130 km//h` (b) The initial velocity of P relative to alex is `v_(PA) = -78 km//h` and the final velocity is 0 . thus , the acceleration relative to alex is `a_(PA) = (v - v_0)/(t ) = (0 - (-78 km //h))/(10 s)(1m//s)/(3.6 km//h)` ` = 2.2 m//s^2` `a_(PA) = (v - v_0)/(t ) = (-25 km//h) - (-130 km//h))/(10 s) (1m//s)/(3.6 km//h)` ` = 2.2 m//s^2` |
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