Answer
The speed that the tongue acquires is $~~5.0~m/s$
Work Step by Step
To find the speed that the tongue acquires, we can find the area under the acceleration versus time curve.
We can divide this area into four parts, including a triangle ($0.01~s$ to $0.02~s$), a rectangle ($0.02~s$ to $0.03~s$), a triangle ($0.02~s$ to $0.03~s$), and a triangle ($0.03~s$ to $0.04~s$)
We can calculate each area separately:
$A_1 = \frac{1}{2}(0.01~s)(100~m/s^2) = 0.50~m/s$
$A_2 = (0.01~s)(100~m/s^2) = 1.0~m/s$
$A_3 = \frac{1}{2}(0.01~s)(300~m/s^2) = 1.5~m/s$
$A_4 = \frac{1}{2}(0.01~s)(400~m/s^2) = 2.0~m/s$
We can find the total area for $t=0~ms$ to $t=40~ms$:
$A = (0.50~m/s)+(1.0~m/s)+(1.5~m/s)+(2.0~m/s)$
$A = 5.0~m/s$
The speed that the tongue acquires is $~~5.0~m/s$
