Question

if a driver of a 500 kg car, heading direcly for a RR crossing 300 m away, applies the brakes in a panic stop. the car is initially moving at 40 m/sec and the brakes are capable of producing a force of 1200 N
(A) how fast will the car be moving when it reaches the crossing?
(B) will the driver escape collision with a freight train that at the instant the brakes are applied is blocking the road, and still requires 11 sec to clear the crossing?

Answer 1

\[\left(\begin{matrix}f \\ m\end{matrix}\right) =a\]
\[\left(\begin{matrix}1200 \\ 300\end{matrix}\right)=2.4\] this is what i think is the decelration of the car when it uses the brakes
\[\left(\begin{matrix}d \\ s\end{matrix}\right)=t\] to find the time taken to reach the RR crossing
\[\left(\begin{matrix}300 \\ 40\end{matrix}\right)=7.5 \sec\]
(A) so i multiply time by decelartion to get the speed when it reaches the crossing
(B) the driver won't servive the accedint because hes not going to stop when he reaches the crossing

Answer 2

\[\Large \begin{array}{l}
F = ma\\
{v^2} = {u^2} + 2as\\
v = u + at\\
F = 1200{\rm{N}}\\
a = \frac{F}{m} = \frac{{1200}}{{500}} = 2.4{\rm{m}}{{\rm{s}}^{ - 2}}\\
s = 300{\rm{m}}\\
v = \sqrt {{{40}^2} + 2 \cdot - 2.4 \cdot 300} = 12.65{\rm{m}}{{\rm{s}}^{ - 1}}\\
t = \left| {\frac{{v - u}}{a}} \right| = \left| {\frac{{12.65 - 40}}{{2.4}}} \right| = 11.40{\rm{s}}
\end{array}\]
So yes, it will miss the train if it takes 11 seconds for it to clear the crossing - just.

Answer 3

well atleast i gave it a try :)

Answer 4

And that's what counts ;) For basic kinematics such as this, probably the trickiest thing is learning which equations to apply and how. If you write down the kinematic equations and keep them handy, then when you're solving a problem just whip them out and deduce which equation relates the variables you do know to each other, and go from there.

Answer 5

so you used the \[v^{2} =u^{2}+2as because you have the distance but you don't have the time?

Answer 6

\[v^{2} =u^{2}+2as \]

Answer 7

Basically; I had the other variables, u, a and s, but needed to know v, so that was precisely the equation I needed without any rearranging necessary.

Answer 8

well that helped alot thanks =)

Answer 9

No worries ;)