A particle moves in a straight line so that, $$ t $$ seconds after leaving a fixed point O , its velocity, $$ v \mathrm{~m} / \mathrm{s} $$, is given by $$ v=\mathrm{e}^{2 t}-4 \mathrm{e}^{t}+12 $$. (i) Find the time at which the particle has a velocity of $$ 17 \mathrm{~m} / \mathrm{s} $$. (ii) Is the acceleration of the particle always positive? How can you tell?

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Deleon Clarke · Accepted Answer

(i) The particle has a velocity of 17 m/s at approximately 1.609 seconds. (ii) The acceleration is not always positive. It is positive when $$ t > \ln(2) $$ seconds and negative when $$ t < \ln(2) $$ seconds.

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