A particle’s displacement, r metres, with respect to time, t seconds, is defined by the equation $r = 3e^{0.5t}$ Find an expression for the velocity, v m s^-1, of the particle at time t seconds - AQA - A-Level Maths Mechanics - Question 11 - 2021 - Paper 2

To find the velocity of the particle, we need to differentiate the displacement equation with respect to time. Given:

$r = 3e^{0.5t}$

We can find the velocity, $v$, by taking the derivative:

$v = \frac{dr}{dt}$

Using the chain rule, we differentiate:

$v = 3 \cdot 0.5e^{0.5t} = 1.5e^{0.5t}$

Thus, the expression for the velocity of the particle at time $t$ seconds is:

$v = 1.5e^{0.5t}$

This is the correct answer to circle.