Question
Asked Nov 14, 2019
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Q 10 Show that for motion in a straight line with constant acceleration a, initial
velocity vo , and initial displacement so, the displacement after time a is
at2
S= So + vot+
2
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Q 10 Show that for motion in a straight line with constant acceleration a, initial velocity vo , and initial displacement so, the displacement after time a is at2 S= So + vot+ 2

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Expert Answer

Step 1
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We have given the acceleration a(t) a, initial velocity v(0) v, and the initial displacement s(0) = s0

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Step 2
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Velocity (v) is the antiderivative of acceleration (a) i.e. v'(t a Integrating, v(t)atC (1) Now v(0) C v = C Substituting C v, in (1) v(t) at +o

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Step 3
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Displacement(s) is the antiderivative of velocity(v) i.e. s'(t) v We have s'() at + Integrating, votD-(2) Now s(0)a( (0)D s = D Substituting D $6 in (2), s(t)at + S

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