# A bus starts from rest with a constant acceleration 2

A bus starts from rest with a constant acceleration of 1 m/$s^2$. Determine the time required for it to attain a speed of 25 m/s and the distance traveled.

#### Solution:

To figure out the time the bus traveled, we will use the following equation:

$v_2=v_1+a_ct$

(Where $v_2$ is final velocity, $v_1$ is initial velocity, $a$ is constant acceleration and $t$ is time)

From the question, the following are given to us:

$v_2=25$ m/s

$v_1=0$ m/s

$a_c=1$ m/$s^2$

Substitute these values into our equation and solve for $t$.

$v_2=v_1+a_ct$

$25=0+1(t)$

$t=25$ s

To figure out the distance traveled, we will use this equation:

$v_2^2=v_1^2+2a_c(s_2-s_1)$

(Where $v_2$ is final velocity, $v_1$ is initial velocity, $a_c$ is constant acceleration, $s_2$ is final displacement, and $s_1$ is initial displacement)

Again, we will substitute the values we know (note that $s_1=0$ m because the original location is our point of reference).

$v_2^2=v_1^2+2a_c(s_2-s_1)$

$25^2=0+2(1)(s_2-0)$

$s_2=312.5$ m