When does the jam start?

Classical Mechanics Level 3

Imagine a road with two cars, each of length $L$ . Car 1 gets on the road at $t = 0$ moving at $v_{1}$ , and car 2 gets on the road at $t = t_{2}$ , moving at $v_{2} > v_{1}$ .

At what time does the front of car 2 to get in contact with the back of car 1?

Solve for the case where

$v_{1} = 20\text{ m/s}, v_{2} = 25 \text{ m/s}, t_{2} = 100 \text{ s}$ , and $L = 5 \text{ m}$ .

Express your answer in seconds.

The answer is 499.

1 solution

Adam Strandberg
Feb 23, 2016

The positions of the front of each of the cars is given by $x_{1} = v_{1} t$ $x_{2} = v_{2} (t - t_{2})$ , when $t > t_{2}$ .

To solve for the case where the back of car 1 is at the same position as the front of car 2, we set

$x_{1} - L = x_{2}$ $v_1 t - L = v_2 (t - t_2)$ $(v_1 - v_2) t = L - v_2 t_2$ $t = \frac{v_2 t_2 - L}{v_2 - v_1}$

Plugging in the values given in the problem, we have: $t = \frac{25 * 100 - 5}{25 - 20}$ $t = 499$

Nice solution! ( By the way you just answered this question at around 3 in the morning in our time!)

Akhash Raja Raam - 5 years, 3 months ago

When does the jam start?

The answer is 499.

1 solution

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