Question

fill in the blank question
in an investigation of how forces affect an objects acceleration, the time graphs for different tests at different constant forces are straight
lines through the graphs origin with different slopes.
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Explanation:

When an object is under a constant force, according to Newton's second law \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration), if the mass \(m\) is constant, the acceleration \(a\) is constant. The kinematic equation for velocity \(v=v_0 + at\). If the initial velocity \(v_0 = 0\) (assuming the object starts from rest, which is a common assumption in such basic force - acceleration investigations), then \(v = at\). This is a linear equation of the form \(y = kx\) (where \(y = v\), \(k=a\), \(x = t\)). So the velocity - time (\(v - t\)) graph is a straight line passing through the origin (\(v_0 = 0\)) and the slope of the \(v - t\) graph is equal to the acceleration \(a\) (since \(a=\frac{\Delta v}{\Delta t}\)). Different constant forces (with the same mass) will result in different accelerations, thus different slopes of the \(v - t\) graphs.

Answer:

velocity