Question

Initially a car accelerates at 2 m/s2 for x seconds. The car then travels at a velocity of -6 m/s for x seconds. If the car displaced a total of 16 m, how long did it travel?

Answer 1

The time travel is

t=8 s

Step-by-step explanation:

`a= 2 (m)/(s^(2) ) \\v=-6 (m)/(s) \\x=16m`

`x_(f)=x_(o)+v_(o)*t+(1)/(2) *a*t^(2)`

`x_(f)=0-6*t+(1)/(2) *2*t^(2)`

`t^(2)-6*t-16=0\\ using :\\\frac{-b+/-\sqrt{b^(2)-4*c*a } }{2} \\\frac{-(-6)+/-\sqrt{(-6)^(2)-4*(-16)*(1) } }{2}=(3)/(2) +/- (10)/(2) \\t_(1) = 2s \\t_(2) = 8s`

Check

`t_(2)=8s`

`x_(f)=x_(o)+v_(o)*t+(1)/(2) *a*t^(2)`

`x_(f)=0-6*+(1)/(2) *2*8^(2)`

`x_(f)=-48+64\\x_(f)=16`