2. 1D Motion / Kinematics

High-speed motion pictures ($3500$ frames/second) of a jumping, $210–μg$ flea yielded the data used to plot the graph in Fig. E$2.54$. (See 'The Flying Leap of the Flea' by M. Rothschild, Y. Schlein, K. Parker, C. Neville, and S. Sternberg in the November $1973$ Scientific American.) This flea was about $2$ mm long and jumped at a nearly vertical takeoff angle. Use the graph to answer this question: Find the flea's acceleration at $0.5$ ms, $1.0$ ms, and $1.5$ ms.

High-speed motion pictures ($3500$ frames/second) of a jumping, $210–μg$ flea yielded the data used to plot the graph in Fig. E$2.54$. (See 'The Flying Leap of the Flea' by M. Rothschild, Y. Schlein, K. Parker, C. Neville, and S. Sternberg in the November $1973$ Scientific American.) This flea was about $2$ mm long and jumped at a nearly vertical takeoff angle. Use the graph to answer this question: Find the maximum height the flea reached in the first $2.5$ ms.

High-speed motion pictures ($3500$ frames/second) of a jumping, $210\text{–}\mu g$ flea yielded the data used to plot the graph in Fig. E$2.54$. (See 'The Flying Leap of the Flea' by M. Rothschild, Y. Schlein, K. Parker, C. Neville, and S. Sternberg in the November $1973$ Scientific American.) This flea was about $2$ mm long and jumped at a nearly vertical takeoff angle. Use the graph to answer this question: Is the acceleration of the flea ever zero? If so, when? Justify your answer.

The table shows test data for the Bugatti Veyron Super Sport, the fastest street car made. The car is moving in a straight line (the $x$-axis).

(a) Sketch a $v_x$-$t$ graph of this car's velocity (in mi/h) as a function of time. Is its acceleration constant?

(b) Calculate the car's average acceleration (in m/s2) between (i) $0$ and $2.1$ s; (ii) $2.1$ s and $20.0$ s; (iii) $20.0$ s and $53$ s. Are these results consistent with your graph in part (a)? (Before you decide to buy this car, it might be helpful to know that only $300$ will be built, it runs out of gas in $12$ minutes at top speed, and it costs more than $\$1.5$ million!)