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?

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Solution:

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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

Final Answers:

Time for the car to reach 120 km/h = 29.8 seconds

Distance traveled during this time = 792 m

Traveling with an initial speed of

Solution:

Final Answers:

This question can be found in Engineering Mechanics: Dynamics, 13th edition, chapter 12, question 12-4.

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