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 ms\(^-1\), of the particle at time t seconds - AQA - A-Level Maths Pure - Question 11 - 2021 - Paper 2

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

The given displacement equation is:

$r = 3e^{0.5t}$

The velocity, v, is defined as the rate of change of displacement with respect to time, which can be expressed mathematically as:

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

Now, we differentiate the displacement function:

$\frac{dr}{dt} = 3 \cdot 0.5e^{0.5t}$

Simplifying this gives:

$v = 1.5e^{0.5t}$

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

$v = 1.5e^{0.5t}$

This is the required answer.