A bicyclist starts from rest and after traveling


A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h. Determine his acceleration if it is constant. Also, how long does it take to reach the speed of 30 km/h?

Solution:

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As the acceleration of the bicyclist is constant, we can use the following equation to solve for it.

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)

 

The following are given to us in the question:

v_2=30 km/h = 8.33 m/s

v_1=0 km/h

s_2=20 m

s_1=0 m

 

Let us substitute these values into our equation and solve for a_c.

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

8.33^2=0+2(a_c)(20-0)

a_c=1.73 m/s^2

 

To figure out the time to reach a speed of 30 km/h, we will use the following equation:

v_2=v_1+a_ct

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

 

Again, substituting the values gives us:

v_2=v_1+a_ct

8.33=0+(1.73)(t)

(remember we found the acceleration)

t=4.8 s

 

Final Answers:

Acceleration = 1.73 m/s^2

Time to reach a speed of 30 km/h = 4.8 s

 

This question can be found in Engineering Mechanics: Dynamics, 13th edition, chapter 12, question 12-7.

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