# A car starts from rest and moves along the $x-axis$ with constant acceleration $5\ ms^{-2}$ for 8 seconds. If it then continues with constant velocity, what distance will the car cover in 12 seconds since it started from the rest?

Given: A car starts from rest and moves along the x-axis with a constant acceleration of 5 m/sfor 8 seconds

To find:  what distance will the car cover in 12 seconds since it started from rest

Solution:

We know that,

$s\ =\ ut\ +\ \frac{1}{2} at^{2}$

But given that, the initial velocity is zero. Therefore, the distance covered by the car in first 8 seconds is

=> $s\ =\ 0\ +\ \frac{1}{2} \times 5\ \times 8^{2}$

=> $s\ =\ 160\ metres$

Therefore, the velocity attained at the end of 8 seconds is:

from, $v\ =\ u\ +\ at$

=> $v=\ 0\ +\ 5\ \times \ 8\ =\ 40\ m/s$

Therefore, since the car has moved with constant velocity from 8th second to 12 second, the distance traveled is

$s\ =\ v\ \times \ t\ =\ 40\ \times \ 4\ =\ 160\ m$.

Therefore, the total distance traveled is $160\ +\ 160\ =\ 320m$

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