Chapter 3.2, Problem 30PP

To determine

The distance covered by the bicycle rider.

Answer to Problem 30PP

  $1161\text{m}$

Explanation of Solution

Given:

Acceleration, $a=2{\text{m/s}}^2$

Speed, $v_f=18\text{m/s}$

Initial velocity, $v_i=0$

Time, $t=1\min =60\text{ s}$

Formula used:

Using kinematics equation of motion

  $v_f^2-v_i^2=2ad$

Where,

  $v_f$ is the final velocity

  $v_i$ is the initial velocity

  $a$ is the acceleration

  $d$ is the distance travelled

Calculation:

Distance travelled by the rider while going down the hill is:

  $\begin{array}{l}{v}_f^2-v_i^2=2ad\\ d=\frac{{18}^2-0^2}{2\left(2\right)}\\ d=81\text{m}\end{array}$

Distance travelled by the rider at the bottom of the hill with maintaining the final velocity of $60\text{s}$ is

  $\begin{array}{l}d\text{'}=v_{f}t\\ d\text{'}=18\times 60\\ d\text{'}=1080\text{m}\end{array}$

Total distance travelled by the rider is

  $\begin{array}{l}{d}_{total}=d+d\text{'}\\ d_{total}=81+1080\\ d_{total}=1161\text{m}\end{array}$

Conclusion:

Therefore, the total distance travelled by the rider is 1161 m.