Chapter 2, Problem 10Q

Two cars emerge side by side from a tunnel. Car A is traveling with speed of 60 km/h and has an acceleration of 40 km/h/min. Car B has a speed of 40 km/h and has an acceleration of 60 km/h/min. Which car is passing the other as they come out of the tunnel? Explain your reasoning.

To determine

The car which passes the other as they come out from the tunnel.

Answer to Problem 10Q

Solution:

Car A will come out first from the tunnel.

Explanation of Solution

Given:

Speed of car A is $60\text{km/h}$

Speed of car B is $40\text{km/h}$

Acceleration of car A is $40{\text{ km/h/min = 2400 km/h}}^2$

Acceleration of car B is $60{\text{ km/h/min = 3600 km/h}}^2$

Formula Used:

Final velocity can be calculated using the first equation of motion:

  $v=u+at$

Where, u is the initial velocity, a is the acceleration and t is the time.

Calculation:

Consider time $t=0$ when the cars just pass each other.

Compare the final velocities in the time interval t.

  $\begin{array}{l}{v}_A=u_A+a_{A}t\\ v_A=60+2400t\\ v_B=u_B+a_{B}t\\ v_B=40+3600t\end{array}$

Though car B has larger acceleration, but at $t=0$ , car A has higher velocity. This means that, when the car just comes out of the tunnel, car A will pass the car Bas they come out from the tunnel. Later on in the journey, car B will overtake car A as it has larger acceleration.

Conclusion:

Thus, the car A will initially come out of the tunnel as it is traveling at a speed of 60 km/hr.