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