MHB How far will the car travel in 10 seconds

karush
Gold Member
MHB
Messages
3,240
Reaction score
5
$\tiny{Embry-Brittle \, 12}$
$\textsf{A car, starting from rest, accelerates in a straight line at a constant rate of $\displaystyle 2.0 \frac{m}{s^2}$}$$\textit{How far will the car travel in $10$ seconds}$\begin{align*}\displaystyle
\Delta t&=10\\
a&=2\\
d_i&=0\\
v_i&=0\\
d_f&= d_i + v_i\Delta t + \frac{1}{2} a \Delta t^2\\
&=0+0\cdot 10+\frac{1}{2} \cdot 2\cdot 10^2\\
&=\color{red}{100 \, m}
\end{align*}no answer given so hope this is ok :cool:
 
Mathematics news on Phys.org
karush said:
$\tiny{Embry-Brittle \, 12}$
$\textsf{A car, starting from rest, accelerates in a straight line at a constant rate of $\displaystyle 2.0 \frac{m}{s^2}$}$$\textit{How far will the car travel in $10$ seconds}$\begin{align*}\displaystyle
\Delta t&=10\\
a&=2\\
d_i&=0\\
v_i&=0\\
d_f&= d_i + v_i\Delta t + \frac{1}{2} a \Delta t^2\\
&=0+0\cdot 10+\frac{1}{2} \cdot 2\cdot 10^2\\
&=\color{red}{100 \, m}
\end{align*}no answer given so hope this is ok :cool:

$\displaystyle \begin{align*} v &= \int{ a\,\mathrm{d}t} \\ v &= a\,t + C_1 \\ v &= a\,t \textrm{ since the car starts from rest...} \\ x &= \int{ v\,\mathrm{d}t} \\ x &= \int{ a\,t \, \mathrm{d}t } \\ x &= \frac{1}{2}\,a\,t^2 + C_2 \textrm{ where } C_2 \textrm{ is the starting position...} \end{align*}$

So with $\displaystyle \begin{align*} t = 10 \textrm{ and } a = 2 \end{align*}$ we have

$\displaystyle \begin{align*} x &= \frac{1}{2} \cdot 2 \cdot 10^2 + C_2 \\ &= 100 + C_2 \end{align*}$

Thus the car has traveled 100 metres.
 
ok
I didn't know you could us a integral on it:cool:why did you shift from $v=$ to $x=$
 
Last edited:
You could use the kinematic equation:

$$x=\frac{v_f^2-v_i^2}{2a}=\frac{\left(20\frac{\text{m}}{\text{s}}\right)^2-\left(0\frac{\text{m}}{\text{s}}\right)^2}{2\left(2\frac{\text{m}}{\text{s}^2}\right)}=100\text{ m}$$
 
karush said:
why did you shift from $v=$ to $x=$

$v$ is velocity, $x$ is position.
 
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