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:

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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

 

Final Answers:

Time required to attain 25 m/s = 25 s

Distance traveled = 312.5 m

 

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

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