Question 12

12. [Maximum mark: 9]

An engineer’s model for an object’s motion is that its acceleration, $\frac{dv}{dt}$, is proportional to $v^{1.5}$, where $v$ is its velocity measured in ms$^{-1}$.

(a) Write down a differential equation based on the engineer’s belief. [1]

The initial velocity of the object is 4 ms$^{-1}$ and its initial acceleration is -3 ms$^{-2}$.

(b) Use the engineer’s model to find an expression for the velocity of the object after $t$ seconds. [8]