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?

Traveling with an initial speed of

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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

 

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

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