Question

Problem 3 (a) You and a friend are bicycling from Springdale to Bentonville. You maintain a constant speed for the entire distance of the trip. Your friend, however, goes 1mph faster than you for the first half of the time to Bentonville and 1mph slower than you for the second half of the time. Who gets to Bentonville first? Explain your reasoning. Wou ld your answer have been different if I had specified the different velocities for 1/2 of the distance instead of the time? (b) A few days later your friend challenges you to a 100m dash. You gladly accept because you know that you can easily outrun your friend. In the middle of the dash, however, something gets stuck to your shoe and you must briefly stop to get it off. The graph below shows the velocity-time curves for you and your friend; both of you continue to run beyond the finish to cool off. She wins. How can you tell? (c) Using this same graph, which one of you had the greatest acceleration, and when? (You can just mark it on the graph if you want to.) Explain how you got this answer, and estimate the magnitude of the acceleration 100 m Dash 10 Fi 10 40(S) 20 30

Answer 1

Suppose total distance is 2d and you travel on it with constant velocity of V then time t_1 = 2d/V Now if your friend is moving in first half (V + 1)mph and (V - 1)mph in second half hence t_2 = d/V + 1 + d/V - 1 = 2dV/V^2 - 1 = 2d/(V - 1/V) hence we can see that time taken by your friend is more as value of (V - 1/V) is less than V t_2 > t_1 Friend time > your time