A car is moving 14.4 m/s when it hits the brakes. It slow from 78.8 m, which take 9.92s. It then accelerates at 1.83 m/s 2 for 4.50 s. What is the total displacement?

 x_total = 104m

Explanation:

This is an exercise in kinematics that we must solve in parts, since there are different steps

first part when it's slowing down

where they indicate the initial speed of the vehicle vo = 14.4 m / s, the distance it travels (x1 = 78.8m) and the time it takes to travel this distance, let's find the final speed of this interval

we seek acceleration

         x = v₀ t - ½ a t²

         a = (x - v₀ t) 2 / t²

let's calculate

         a = (78.8 - 14.4 9.92) 2 / 9.92²

         a = -1,302 m / s²

the sign indicates that the acceleration is against the speed

         v = v₀ - a t

         v = 14.4 -1,302 9.92

         v = 1,487 m / s

it is at speed so it starts at second acceleration interval

          x₂ = v₀ t + ½ a t²

          x₂ = 1,487 4.5 + ½ 1.83 4.5²

          x₂ = 25.22 m

whereby the total displacement is

          x_total = x₁ + x₂

         x_total = 78.8 + 25.22

        x_total = 104m