Consider an object weighing m (kg) which is initially at rest and experiences a

Question

Consider an object weighing m (kg) which is initially at rest and experiences a
constant acceleration of a (m/s2) for a duration of t (s). Express your answer
to each of the following questions in the form of an equation involving only the
variables m, a and t (neglecting the effects of friction). [Hint: Integrate the
acceleration to obtain the velocity and then integrate the velocity to obtain the
distance traveled.]
a) What is the force on the object?
b) What is the final velocity of the object?
c) What is the final distance that the object has traveled?
d) Show that the total work performed on the object is exactly equal to its
nal kinetic energy.

Explanation / Answer

a) Force is proportional to the mass and acceleration of an object: F = ma b) v = Integral(a dt) v = at c) d = Integral(v dt) d = Integral(at dt) d = at^2/2 d = 0.5at^2 d) Work = F*d Work = (ma)(0.5at^2) Work = 0.5m(a^2)(t^2) KE = 0.5mv^2 KE = 0.5m(at)^2 KE = 0.5m(a^2)(t^2) KE = Work BOL

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