Answer
The speed of the torso is $~~3.9~m/s$
Work Step by Step
The maximum head acceleration occurs at $t = 160~ms$
To find the speed of the torso, we can find the area under the acceleration versus time curve for the torso. We can divide this area into four parts which includes a triangle ($40~ms$ to $100~ms$), a rectangle ($100~ms$ to $120~ms$), a triangle ($120~ms$ to $160~ms$), and a rectangle ($120~ms$ to $160~ms$)
We can calculate each area separately:
$A_1 = \frac{1}{2}(0.060~s)(50~m/s^2) = 1.5~m/s$
$A_2 = (0.020~s)(50~m/s^2) = 1.0~m/s$
$A_3 = \frac{1}{2}(0.040~s)(30~m/s^2) = 0.6~m/s$
$A_4 = (0.040~s)(20~m/s^2) = 0.8~m/s$
We can find the total area:
$A = (1.5~m/s)+(1.0~m/s)+(0.6~m/s)+(0.8~m/s)$
$A = 3.9~m/s$
The speed of the torso is $~~3.9~m/s$.
