A particle with velocity at any time t is given by v(t)=2e^{2t} moves in a straight line. How far does the particle travel during the time interval when its velocity increases from 2 to 4?

A particle with velocity at any time t is given by v(t)=2e^{2t} moves in a straight line. How far does the particle travel during the time interval when its velocity increases from 2 to 4?

Question
Integrals
asked 2021-03-07
A particle with velocity at any time t is given by \(\displaystyle{v}{\left({t}\right)}={2}{e}^{{{2}{t}}}\) moves in a straight line. How far does the particle travel during the time interval when its velocity increases from 2 to 4?

Answers (1)

2021-03-08
Given that the velocity of a particle at any time t is given by
\(\displaystyle{v}{\left({t}\right)}={2}{e}^{{{2}{t}}}\)
and it is moving in the straight line we have to find the displacement. Integrate the above Equation between the limits 2 to 4
Then
\(\displaystyle{s}={\int_{{2}}^{{4}}}{2}{e}^{{{2}{t}}}{\left.{d}{t}\right.}\)
\(\displaystyle={2}{{\left[{\frac{{{e}^{{{2}{t}}}}}{{{2}}}}\right]}_{{2}}^{{4}}}\)
\(\displaystyle={e}^{{8}}-{e}^{{4}}\)
0

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