# A truck, traveling along a straight road

A truck, traveling along a straight road at speed 20 km/h, increases its speed to 120 km/h in time 15 s. If its acceleration is constant, determine the distance traveled.

#### Solution:

Let us first write the given speeds in base SI units.

20 km/h = 5.5 m/s

120 km/h = 33.3 m/s

We will now find the acceleration of the truck during the 15 second interval. We require the acceleration to figure out the distance traveled. We can use the following equation to find the acceleration since it is constant.

$v=v_0+at$

(Where $v$ is final velocity, $v_0$ is initial velocity, $a$ is acceleration, and $t$ is time)

Let us substitute the values we know.

$v=v_0+at$

$33.3=5.5+a(15)$

(Solve for a)

$a=1.85$ m/$s^2$

We can now find the distance traveled using another kinematic equation.

$x=x_0+v_0t+\dfrac{1}{2}at^2$

(Where $x$ is final displacement, $x_0$ initial displacement, $v_0$ is initial speed, $a$ is acceleration, and $t$ is time)

Let us substitute the values we know.

$x=x_0+v_0t+\dfrac{1}{2}at^2$

$x=0+(5.5)(15)+\dfrac{1}{2}(1.85)(15^2)$

(Here, $x_0$ is 0 because we will consider it to be our origin)

$x=290.6$ m

Thus, the trucked traveled 290.6 m within 15 seconds.