Chameleons catch insects with their tongues, which they can rapidly extend to great lengths. In a typical strike, the chameleon's tongue accelerates at a remarkable 210 m/s^2 for 20 ms, then travels at constant speed for another 30 ms. During this total time of 50 ms, 1/20 of a second, how far does the tongue reach?
Express your answer to two significant figures and include the appropriate units.

  x_total = 0.17m

Explanation:

We can treat this exercise with the kinematics equations, where in the first part it is accelerated and in the second it is a uniform movement.

Let's analyze accelerated motion

The time that lasts is t = 20 10⁻³ s, the initial speed is zero (v₀ = 0), let's find the length that advances

            x₁ = v₀ t + ½ a t²

            x₁ = ½ a t²

            x₁ = ½ 210 (20 10⁻³)²

            x₁ = 4.2 10⁻² m

let's find the speed for the end of this movement

            v = v₀ + a t

            v = 0 + 210   20 10⁻³

            v = 4.2 m / s

with this speed we can find the distance that the uniform movement

           x₂ = v t2

           x₂ = 4.2   30 10⁻³

           x₂ = 1.26 10⁻¹ m

           x₂ = 0.126m

the total distance traveled is

          x_total = x₁ + x₂

          x_total = 0.0420 +0.126

          x_total = 0.168m

     Let's reduce the significant figures to two

          x_total = 0.17m