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# You are thrown from a bicycle and skid in a straight line to a complete stop on a rough road at t a distance of 3.5 m along a straight line. What average force did the road exert on your body if your mass is 70 kg and your initial speed was 30 km/h?

To calculate the Force, we need to first calculate the acceleration, as we are given the mass.
We are given enough kinematic data to determine the acceleration. We can use the Time Independent Acceleration Equation $v_f^2 - v_0^2 = 2ad$
In this case we know the final velocity, original velocity, and displacement, we can now calculate the acceleration.
The final velocity is 0 km/h as the bike (and you) come to a halt slowly. Displacement is 3.5m, and the initial velocity is given as 30 km/h (which is 8.33 m/s)
$\Rightarrow 0^2 - (8.33)^2 = 2 \times a \times 3.5m \rightarrow a = -9.92\; m/s^2$ (the minus sign indicates your deceleration or slowing down).
From Newton's 2nd law, $F = ma = 70 \times -9.92 = -694\; N$ ( minus sign means the force is opposite to the direction of initial motion)
edited Aug 19, 2014