<p>The velocity, \(\mathrm{v}\), in m s\(^{-1}\) of a particle moving in a straight line is given by \(\mathrm{v}=e^{3t-2}\), where&nbsp;\(t\) is the time in seconds.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the acceleration of the particle at \(t=1\).</div></li><li><div class="list-item-paragraph">At what value of \(t\) does the particle have a velocity of \(22.3\) m s\(^{-1}\)?</div></li><li><div class="list-item-paragraph">Find the distance travelled in the first second.<span class="inline-marks">[6]</span></div></li></ol>

The velocity, \(\mathrm{v}\), in m s\(^{-1}\) of a particle moving in a straight line is given by \(\mathrm{v}=e^{3t-2}\), where \(t\) is the time in seconds.

Find the acceleration of the particle at \(t=1\).

At what value of \(t\) does the particle have a velocity of \(22.3\) m s\(^{-1}\)?

Find the distance travelled in the first second.

Mathematics

International Baccalaureate Mathematics: Applications and Interpretation Standard Level