Mathematics

Mathematics

Problem

The velocity of a particle moving along a line is given by v(t)=t2−4t+3v(t)=t^{2}-4t+3 for 0 ≤ t≤50\text{\,}\le\,t\le5. Determine all time(s) in the interval when the particle changes direction. a) t=2t=2 b) t=1 onlyt=1\,\text{only} c) t=1 and t=3t=1\,\text{and}\,t=3 d) The particle does not change direction on [0,5][0,5]
Intuitive explanation

The particle changes direction whenever its velocity switches sign—that's when it stops and reverses course. To find these moments, set v(t)=0v(t) = 0 and solve for tt, then check which solutions fall in your interval. The key insight is that direction changes happen at the zeros of the velocity function, not where acceleration is zero.

Intuitive explanation

The particle changes direction whenever its velocity switches sign—that's when it stops and reverses course. To find these moments, set v(t)=0v(t) = 0 and solve for tt, then check which solutions fall in your interval. The key insight is that direction changes happen at the zeros of the velocity function, not where acceleration is zero.

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