1. ## non uniform acceleration

I have the following question,

A car starts from rest and moves in a straight line in the manner descibed below:

Period 1 0 to 4s the acceleration is non uniform i.e after 1s the aceleration is 1m/s after 2 secs the aceleration is 2m/s

period 2 t=4-6 the velocity is constant

period 3 from t=6-10 the car brakes uniformly to rest

calculate the total distance the car travelled after 10 secs

I can work out period 2 and 3 but theres nothing in my book about non uniform acceleration.

2. Period 1 0 to 4s the acceleration is non uniform i.e after 1s the aceleration is 1m/s after 2 secs the aceleration is 2m/s
no other info about about the interval t = 0 to t = 4 other than v(0) = 0 and the above?

there are many models for non-uniform acceleration that one can come up with to fit the given data ...

here's a simple one

$\displaystyle a(t) = t \,\,, \,\, 0 \leq t < 4$

I'm sure that someone else can come up with other models for acceleration that will fit.

3. Thats all the information given in the question, forgive me, but i cant understand how to use what you given me

4. in the interval, $\displaystyle 0 \leq t < 4$ , if $\displaystyle a(t) = t$ and $\displaystyle v(0) = 0$, then you can come up with a velocity function for that time interval.

$\displaystyle v(t) = \int t \, dt$

$\displaystyle v(t) = \frac{t^2}{2} + C$

since $\displaystyle v(0) = 0$ ...

$\displaystyle v(t) = \frac{t^2}{2} \, \, , \, \, 0 \leq t < 4$

on the interval, $\displaystyle 4 \leq t < 6$ ... (velocity is constant)

$\displaystyle v(t) = 8$

on the interval, $\displaystyle 6 \leq t \leq 10$

$\displaystyle v(t) = 20 - 2t$

total distance traveled ...

$\displaystyle d = \int_0^4 \frac{t^2}{2} \, dt + \int_4^6 8 \, dt + \int_6^{10} 20-2t \, dt$

5. got it now! thanks