A particle moves in a straight line with velocity v=(t-2)2(t-5) m/s at time t seconds, for 0

Question

A particle moves in a straight line with velocity v=(t-2)2(t-5) m/s at time t seconds, for 0 <= t 6. - Show that the acceleration is a=3(t-2)(t-4) m/s2. - Find the time intervals in which the particle is speeding up. - Explain why the particle is at rest at t=2 but does not change direction there.

Accepted Answer

(a) shown (b) $2\lt t\lt4$ and $5\lt t\lt6$ (c) $v\le0$ on both sides of $t=2$, so no change of sign

Speeding up while moving backwards

Speeding up while moving backwards

Solution:

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