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EMPhillips1989

Member

Registered: 2008-01-21

Posts: 40

mechanics please help!!!!

hey can anyone help me out i've attempted to complete a question for revision purposes but i'm not sure what i've done is correct. i'm new to mechanics and was wondering if anyone could possibly point me in the right line

The question is:
A car accelerates from rest to 28m/s in 10 seconds.
by working from first principles find the cars acceleration, and the distance travelled in this time in metres.

My attempt at solving:
the car moves in direction x at constant speed u. after a time, t the car will be at the position:

since the car is acelerating, its speed is no longer constant and now depends on time.  u=u(t)
since velocity is the rate of change of position with time

      [1]
and acceleration is the rate of change of velocity with time

      [2]
intergrating w.r.t time gives:

where c is a constant
since car started at rest when t=0, u=0 therefore c=0

which leaves

To find the acceleration i did:

Now to find the distance travelled in this time i did:

from [1]

integrating this w.r.t time gives:

where d is a constant
when t=0 x=0, therefore d=0
so we get:

using the information given and a=2.8m/s^2

x=140 metres

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: mechanics please help!!!!

Everything there is correct.

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Why did the vector cross the road?
It wanted to be normal.