Physics, 13.01.2020 19:31 king514

The next einstein initiative and the institute for mathematical sciences bring bright young learners and the best lecturers in the world together.

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Answer from: bluetopaz447

African Institute for Mathematical Sciences.

Explanation: The African Institute for Mathematical Sciences (AIMS) is a pan-African network of centres of excellence that enables Africa's talented students to actively become innovators to Foster the educational, economic and also the scientific sector of the continent. This global body aims to encourage breakthrough discoveries with mathematical sciences. It was established in 2003 in the research institute in Muinzenburg, South Africa with other partner bodies in other African countries like Senegal, Cameroon, Ghana etc. The main aim of this body is to; foster economic self-sufficiency, ability to solve global challenges, and also to empower Africa's youth to shape it's future. Their activities span from Research, Training and Public engagement.

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

Answer from: Quest

distance = 150m

displ = root (50 ^2 + 100^2)

root(2500+10000)

root 125000

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