suppose there are two cars black and red .the black car start first and move with uniform acceleration of 3m/s2,after 55seconds the red car starts from rest and move with uniform acceleration of 14m/s2, calculate the distance at which the red car will overtake the black car
d1 = (1/2) 3 t^2
d2= (1/2) 14 (t-55)^2
when does d1= d2 ?
3 t^2 = 14 (t^2 - 110 t + 3025)
11 t^2- 1540 t + 42350 = 0
t = 37.6 or 102.4
37.6 is no good, the red car started 55 seconds ago during negative time
use 102.4 seconds
d1 = (1/2) 3 t^2 = 1.5* 102.4^2 = 15728
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check
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d2 = (1/2)(14) * 47.4^2 = 15727