VERY HARD SUVAT QUESTION - need urgent help please!

A motorist travelling at x m/s joins a motorway. On the motorway she travels at a constant acceleration of 0.07 m/s-2, until her speed has increased by 2.8m/s. Calculate the time for the increase in speed.
(NOTE : IT DOES MENTION LATER IN THE QUESTION THAT THE DISTANCE TAKEN FOR THE CHANGE IN SPEED IS 1050M).

Reply 1

cazual

S = ?
U = x m/s
V = x + 2.8 m/s
A = 0.07 m/s^2
T = ?

Now use one of the equations and rearrange to find the time.

Good luck

Reply 2

RDKGames

Study Forum Helper

Pretty simple.

u=x, v=x+2.8, a=0.07

You know

s=\frac{1}{2}(u+v)t

So use

v^2=u^2+2as=u^2+a(u+v)t

and solve for

t

Reply 3

IGCSETANK

Original post by cazual

S = ?
U = x m/s
V = x + 2.8 m/s
A = 0.07 m/s^2
T = ?

Now use one of the equations and rearrange to find the time.

Good luck

I laid it out exactly like you, yet i achieved an incorrect answer. Could you do it and see what answer you would get. I used the s=ut + 0.5at2, but surely you cant use U as you would then have two unknowns?
Thanks

Reply 4

IGCSETANK

Original post by RDKGames

Pretty simple.

u=x, v=x+2.8, a=0.07

You know

s=\frac{1}{2}(u+v)t

So use

v^2=u^2+2as=u^2+a(u+v)t

and solve for

t

Im pretty sure thats wrong as how would you be able to solve for T if U is unknown?
Thanks

Reply 5

RDKGames

Study Forum Helper

Original post by IGCSETANK

Im pretty sure thats wrong as how would you be able to solve for T if U is unknown?
Thanks

The

x

goes away with basic manipulation if you go through it. I got a nice answer.

Reply 6

cazual

S = ?
U = x m/s
V = x + 2.8 m/s
A = 0.07 m/s^2
T = ?

V = U + AT

x + 2.8 = x + 0.07t
2.8 = 0.07t
t = 40 s

Reply 7

IGCSETANK

Original post by RDKGames

The

x

goes away with basic manipulation if you go through it. I got a nice answer.

Can you display what youve said in different steps and order of logical working, with an answer at the end, because i'm confused as to what your getting at here.
Thank you

40 seconds

Original post by IGCSETANK

Can you display what youve said in different steps and order of logical working, with an answer at the end, because i'm confused as to what your getting at here.
Thank you

I'm sure you understood the post above, it's simple substitution.

So it becomes:

(x+2.8)^2=x^2+0.07t(2x+2.8)

\Rightarrow x^2+5.6x+7.84=x^2+t(0.14x+0.196)

\Rightarrow 5.6x+7.84=(0.14x+0.196)t

\displaystyle \frac{5.6x+7.84}{0.14x+0.196}=t

\displaystyle \frac{5.6x+7.84}{\frac{1}{40}(5.6x+7.84)}=t

and finishing it off leaves you with

t=40

It is easier to notice that the fraction cancels if you turn decimals into fractions, then put everything under a single fraction. Otherwise, use your calculator to investigate what multiple you need.

There is a solution above with