SUVAT equation question: When will the car collide with the lorry?

[lukegxhycj]

Homework Statement

A lorry travelling along a narrow road with speed u1

applies its brakes to give a uniform deceleration of magnitude a1

. At the same time a car, a distance d behind the lorry and travelling in the same direction with speed u2

, applies its brakes to give a uniform deceleration of a2

Part A
Show that the car collides with the now stationary lorry if a2≤ku2^2

, and find k in terms of u1 , d and a1

Relevant Equations

All SUVAT equations

s1=-u1^2/2a1
s2=-u2^2/2a2

s2>s1+d
(If distance the car stops is bigger than the distance the lorry stops plus the initial distance then they will crash)

(sub s1 and s2 in)
-u2^2/2a2 > -u1^2/2a1+d
Switch 2a2 with whole left side of equation.
-u2^2/(-u1^2/2a1)+d > 2a2
Make the (d)a fraction by multiplying denominator and numerator by 2a1
-u2^2*(2a1/-u1^2+2a1d) > 2a2
Cancel the minus time minus on the left side.
u2^2*(a1/u1^2+2a1d)>a2
K=a1/u1^2+2a1d
And it was wrong apparently

 

[berkeman]

Homework Statement: A lorry travelling along a narrow road with speed u1

applies its brakes to give a uniform deceleration of magnitude a1

. At the same time a car, a distance d behind the lorry and travelling in the same direction with speed u2

, applies its brakes to give a uniform deceleration of magnitude a2

.Part A
Requirement on deceleration
All questions in this part are answered incorrectly
Show that the car collides with the now stationary lorry if a2≤ku2^2

, and find k in terms of u1 , d and a1
Relevant Equations: SUVAT equations of motion:
v
2
=u
2
+2as
s=ut+
2
1

at
2

s=
2
u+v

t
v=u+at

(a_1)/(u_1**(2) - d*a_1*2)

Welcome to PF.

Something is really messed up in your equations. Did you paste them in from somewhere? What device and browser are you using to log into PF?

 

[BvU]

Hello @lukegxhycj ,

$\qquad$ !​

Please read the PF guidelines

WIth a bit of $\LaTeX$ your post might look like

Homework Statement: A lorry travelling along a narrow road with speed $u_1$ applies its brakes to give a uniform deceleration of magnitude $a_1$.
At the same time a car, a distance $d$ behind the lorry and travelling in the same direction with speed $u_2$, applies its brakes to give a uniform deceleration of magnitude $a_2$.

Part A
Requirement on deceleration
Show that the car collides with the now stationary lorry if $a_2 ≤ k u_2^2$, and find $k$ in terms of $u_1$, $d$ and $a_1$

Relevant Equations: SUVAT equations of motion:
...

I agree the SUVAT equations are what you need to solve this exercise.
Sort them out with $\LaTeX$ and post your best effort at solution (required per the PF homewok rules)And:

I don't understand how

All questions in this part are answered incorrectly

can be part of the problem statement. Can you explain ?

$\$

 

[lukegxhycj]

Hello @lukegxhycj ,

$\qquad$ !​

Please read the PF guidelines

WIth a bit of $\LaTeX$ your post might look like
I agree the SUVAT equations are what you need to solve this exercise.
Sort them out with $\LaTeX$ and post your best effort at solution (required per the PF homewok rules)And:

I don't understand how can be part of the problem statement. Can you explain ?

$\$

It is an error let me fix it also I am on my phone so I can’t use latex

 

[berkeman]

also I am on my phone so I can’t use latex

Are you sure? I don't remember if I've tried it from my phone, but it seems like it should work. Have you looked at the LaTeX Guide link below the Edit window?

 

[lukegxhycj]

Welcome to PF.

Something is really messed up in your equations. Did you paste them in from somewhere? What device and browser are you using to log into PF?

Yeah sorry I meant to paste all SUVAT equations I’ve fixed it now it doesn’t have them because it messes it up

 

[berkeman]

(a_1)/(u_1**(2) - d*a_1*2)

That's an expression, not an equation. Can you try to show more work on this? I'm not sure why you're having issues typing math into the forum. What kind of phone is it?

 

[lukegxhycj]

That's an expression, not an equation. Can you try to show more work on this? I'm not sure why you're having issues typing math into the forum. What kind of phone is it?

Yh this is the answer I got but it’s wrong

 

[lukegxhycj]

That's an expression, not an equation. Can you try to show more work on this? I'm not sure why you're having issues typing math into the forum. What kind of phone is it?

K=

 

[haruspex]

Yh this is the answer I got but it’s wrong

Then you need to post your working so that we can see where you went wrong.

 

[lukegxhycj]

Then you need to post your working

Then you need to post your working so that we can see where you went wrong.

so that we can see where yowent wrong.

Ok

Then you need to post your working so that we can see where you went wrong.

I have added the working please could you take a look at it thanks for your time

 

[Mark44]

I have added the working please could you take a look at it thanks for your time

Your photos of your work are almost completely illegible, due to poor lighting and mostly faint writing. We generally discourage members from posting photos of their work for these reasons.

 

[berkeman]

I have added the working

And just an FYI for the future, in discussion forums we usually discourage altering your Original Post (OP) with more information that is asked for in subsequent replies, because it is very confusing for folks who read the thread later. It makes our requests for more information look strange, since the extra information is in your OP by the time they read it. It works much better if you add the extra information in a new reply instead. Thanks.

I will send you a Private Message (PM) with tips for using LaTeX to post your work.

 

[nasu]

(If distance the car stops is bigger than the distance the lorry stops plus the initial distance then they will crash)

This condition is not relevant. The car can crash into the lorry before the lorry stops.

 

[lukegxhycj]

Yes sir the the question says the lorry stops before the car

 

[haruspex]

Ok

I have added the working please could you take a look at it thanks for your time

I think you have been inconsistent in the signs on the accelerations. I see "a=-a₁” but "a=a₂".

 

[lukegxhycj]

I think you have been inconsistent in the signs on the accelerations. I see "a=-a₁” but "a=a₂".

Sorry can you please get an answer so I can reverse engineer what I’ve done wrong

 

[erobz]

Sorry can you please get an answer so I can reverse engineer what I’ve done wrong

We don’t give answers; we help you sus out errors. You fix the errors and hopefully you learn.

 

[haruspex]

Sorry can you please get an answer so I can reverse engineer what I’ve done wrong

At top right of your first attachment I see $a=a_2$.
$a_2$ is given as a rate of deceleration, so the acceleration is $-a_2$. You did it correctly for $a_1$.