Back to the full dot-point answer
QLDMath MethodsQuick questions
Unit 4: Further calculus and statistical inference
Quick questions on Area and kinematics applications of integration: QCE Maths Methods Unit 4
10short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is displacement from velocity?Show answer
For a particle with velocity $v(t)$ from $t = t_1$ to $t = t_2$:
What is distance travelled from velocity?Show answer
Total distance is the integral of speed $|v(t)|$:
What is position function from velocity?Show answer
If $v(t) = \frac{dx}{dt}$ and $x(t_0) = x_0$ is the initial position:
What is velocity and position from acceleration?Show answer
$$v(t) = v_0 + \int_{t_0}^{t} a(s) \, ds$$
What is mixing displacement and distance?Show answer
Displacement is the signed integral; distance is the absolute-value integral or the split-and-sum.
What is forgetting to split at zeros of $v$ for distance?Show answer
A particle that changes direction has distance greater than displacement. The split-and-sum is mandatory.
What is top-bottom backwards?Show answer
Picking the wrong "top" gives a negative area. Test a value in each sub-interval before integrating.
What is forgetting the constant of integration in position-from-velocity?Show answer
$x(t)$ has $C$, which must be determined from $x(t_0) = x_0$.
What is average velocity vs average speed?Show answer
Average velocity = displacement / time. Average speed = distance / time. They differ when the particle reverses direction.
What is forgetting to divide by interval length for average value?Show answer
$\bar f = \frac{1}{b-a} \int_a^b f \, dx$; the $\frac{1}{b-a}$ is essential.