Question

practice it!
select the statement(s) that accurately describe the relationship between forces and motion.
an object will travel farther when more force is applied.
less massive objects require stronger forces to move them than more massive objects.
an object will travel faster when more force is applied.
objects with more mass require stronger forces to move them than objects with less mass.
there is no relationship between mass and force.

Explanation:

• According to Newton's second law \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration). If the force \(F\) increases (assuming mass \(m\) is constant), the acceleration \(a=\frac{F}{m}\) increases. A greater acceleration means the object will travel faster (since \(v = v_0+at\), with \(v_0\) initial velocity, \(t\) time). So, an object will travel faster when more force is applied.
• Also from \(F = ma\), if we want to achieve a certain acceleration \(a\), a larger - mass (\(m\)) object requires a larger force \(F\) (because \(F\) is directly proportional to \(m\) when \(a\) is constant). So, objects with more mass require stronger forces to move them than objects with less mass.
• The statement “An object will travel farther when more force is applied” is not always accurate as distance \(d=v_0t+\frac{1}{2}at^2\), and it also depends on time of application of force and initial velocity.
• The statement “Less massive objects require stronger forces to move them than more massive objects” is wrong as \(F = ma\) shows the opposite.
• The statement “There is no relationship between mass and force” is wrong as \(F = ma\) shows a direct relationship.

Answer:

C. An object will travel faster when more force is applied.
D. Objects with more mass require stronger forces to move them than objects with less mass.