MHB Displacement-Time Graph Velocity of Objects X & Y

  • Thread starter Thread starter mathlearn
  • Start date Start date
  • Tags Tags
    Graphs Motion
mathlearn
Messages
331
Reaction score
0
View attachment 6152

The gradient of the displacement time graph is the velocity.

Gradient of x = $\frac{y_1-y_2}{x_1-x_2}=\frac{30-40}{6-12}=\frac{-10}{-6}=\frac{5}{3}$ meters per second

Gradient of y = $\frac{y_1-y_2}{x_1-x_2}=\frac{0-40}{0-8}=\frac{-40}{-8}=5$ meters per second

Therefore the first option is false the second is also so not true, according to my calculations above the fourth option is true,and also it looks like the third is also true as the displacement is equal

Many Thanks :)
 

Attachments

  • displacement.png
    displacement.png
    8.4 KB · Views: 114
Mathematics news on Phys.org
I agree with you on (1), (2) and (4). Concerning (3), displacements are indeed equal at $t=6$. According to Wikipedia, displacement is the difference between the final and initial position vectors. In this problem, apparently, objects move along a line, so instead of vectors we may consider their position $s(t)$ at time $t$ on the line. Suppose displacement is counted relative to some initial time $t_0$. ($t_0$ cannot be 0 because $s_X(0)-s_X(t_0)=20$.) So
\begin{align}
s_X(6)-s_X(t_0)&=30\\
s_X(0)-s_X(t_0)&=20,
\end{align}
from where $s_X(6)-s_X(0)=10$. Similarly, $s_Y(6)-s_Y(0)=30$. The graph shows that the objects did not change the direction, so the distance $X$ traveled between $t=0$ and $t=6$ equals $|s_X(6)-s_X(0)|=10$, while the distance $Y$ traveled is 30.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top