Traveling with an initial speed of

Traveling with an initial speed of 70 km/h, a car accelerates at 6000km/$h^2$ along a straight road. How long will it take to reach a speed of 120 km/h? Also, through what distance does the car travel during this time?

Image from: By ryanlerch (Open Clip Art Library image’s page) [CC0], via Wikimedia Commons

Solution:

To figure out the time it takes for the car to reach 120 km/h, we will use the following formula:

$v_2=v_1+a_ct$

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

From the question, we are given the following:

$v_2=120$ km/h

$v_1=70$ km/h

$a_c=6000$ km/$h^2$

Let us substitute the values into our equation.

$v_2=v_1+a_ct$

$120=70+(6000)(t)$

$t=0.0083\,\text{hrs}=29.8$ s

To find the distance the car travels during this time, we will use the following 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)

Let us substitute the values we know:

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

$120^2=70^2+2(6000)(s_2-0)$

$s_2=0.792\text{km}=792$ m