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In one dimensional motion, instantaneous speed $v$ satisfies $0 \leq \mathrm{v} < \mathrm{v}_0$.
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The displacement $x$ in time $T$ satisfies $-v_0 T < x < v_0 T$
The displacement $x$ in time $T$ satisfies $-v_0 T < x < v_0 T$
In one dimensional motion, for the maximum and minimum displacement we must have the magnitude and direction of maximum velocity.
As maximum velocity in positive direction is $v_0$, hence maximum velocity in opposite direction is also $-v_0$. Maximum displacement in one direction $=v_0 T$ Maximum displacement in opposite directions $={ }_{-\mathrm{v}_0} T$.
Hence, $-v_0 T < x < v_0 T$
As maximum velocity in positive direction is $v_0$, hence maximum velocity in opposite direction is also $-v_0$. Maximum displacement in one direction $=v_0 T$ Maximum displacement in opposite directions $={ }_{-\mathrm{v}_0} T$.
Hence, $-v_0 T < x < v_0 T$
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