Question

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.

Answer 1

x_total = 0.17m

Step-by-step 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