Question

Find the distance travelled by the car if it starts moving from rest and has been travelling for 7 seconds, with the maximum acceleration of 6ms^-2.

Answer 1

Is the acceleration constant?

Answer 2

It's not mentioned.

Answer 3

\[x=1/2(6)7^2\]

Answer 4

Assuming it is:
x=ut+0.5*a*t^2
u=0
x=0.5*6*7^2
x=147m

Answer 5

No, I don't think that's the right way. It's just the max. acceleration..
And this question is from a math quiz, carrying 25 marks.

Answer 6

\[y=0+1/2(at^2)\]
\[a=\frac{ 2y }{ t^2 }\]\[.........................a^'=\frac{ 2y^'t^2-4ty }{ t^4 }\]
\[y=\frac{ v }{ 2t }\]
\[............................y^'=2v \ln t\]
max a
\[0=\frac{ 4vt \ln t -2v}{ t^4 }\]
\[t\ln t=\frac{ 1 }{ 2 }\]
\[t^t=0,5\]

Answer 7

CRAZY

Answer 8

\[ s = \int_{0}^{7} v(t) dt \\
v(t) = \int_0^7 a(t) dt \\
s = \int_0^7 \int_0^7 a(t)\; dt \; dt
\]

Answer 9

and the equation of a(t) is....?

Answer 10

all we know is \( |a(t)| \leq 6 \)

Answer 11

distance can be expressed in terms of inequality ... the distance depends on a(t) so we do not know exactly.

Answer 12

one example of such acceleration would be
\[ a(t) = {-t(t-7)24 \over 49 } \]

Answer 13

But we don't know what a(t) is, how can we integrate that?

Answer 14

you can set a = 6 and express it in terms of inequality. there is no certainty ... is it stat question?

Answer 15

Calculus.

Answer 16

do you have answers?

Answer 17

no.

Answer 18

probably ... answer is in range [from this distance to this distance]

Answer 19

Would it be something related to parametric equations?

Answer 20

ah sorry this would be this
\[
s = \int_{0}^{7} v(t) dt \\
v(t) = \int_0^t a(t) dt \\
s = \int_0^7 \int_0^t a(t)\; dt \; dt \]

Answer 21

@RolyPoly do you know the second eq. of motion

Answer 22

do you know?

Answer 23

@RolyPoly

Answer 24

Under constant acceleration, I know. But sorry that we don't even know if the motion is of constant acceleration!

Answer 25

we can suppose....

Answer 26

We can't! It's a MATH question after all!~

Answer 27

ok sry