Easy -1.8 This is a straightforward single-step differentiation of an exponential function using the chain rule, presented as a multiple-choice question. It requires only direct application of a standard formula (d/dt of e^(kt) = ke^(kt)) with no problem-solving, making it significantly easier than average A-level questions.
11 A particle's displacement, \(r\) metres, with respect to time, \(t\) seconds, is defined by the equation
$$r = 3 \mathrm { e } ^ { 0.5 t }$$
Find an expression for the velocity, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of the particle at time \(t\) seconds.
Circle your answer.
\(v = 1.5 \mathrm { e } ^ { 0.5 t }\)
\(v = 6 \mathrm { e } ^ { 0.5 t }\)
\(v = 1.5 t \mathrm { e } ^ { 0.5 t }\)
\(v = 6 t e ^ { 0.5 t }\)
11 A particle's displacement, $r$ metres, with respect to time, $t$ seconds, is defined by the equation
$$r = 3 \mathrm { e } ^ { 0.5 t }$$
Find an expression for the velocity, $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, of the particle at time $t$ seconds.\\
Circle your answer.\\
$v = 1.5 \mathrm { e } ^ { 0.5 t }$\\
$v = 6 \mathrm { e } ^ { 0.5 t }$\\
$v = 1.5 t \mathrm { e } ^ { 0.5 t }$\\
$v = 6 t e ^ { 0.5 t }$
\hfill \mbox{\textit{AQA Paper 2 2021 Q11 [1]}}