While driving a car at 90 km/h, how far do you move while your eyes shut for 0.50 s during a hard sneeze?

Compute your average velocity in the following two cases: (a) You walk 73.2 m at a speed of 1.22 m/s and then run 73.2 m at a speed of 2.85 m/s along a straight track. (b) You walk for 1.00 min at a speed of 1.22 m/s and then run for 1.00 min at 3.05 m/s along a straight track. (c) Graph x versus t for both cases and indicate how the average velocity is found on the graph.

Two trains, each having a speed of 30 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 60 km apart and heads directly for the other train. On reaching the other train, the (crazy) bird flies directly back to the first train, and so forth. What is the total distance the bird travels before the trains collide?

You drive on Interstate 10 from San Antonio to Houston, half the time at 55 km/h and the other half at 90 km/h. On the way back you travel half the distance at 55 km/h and the other half at 90 km/h. What is your average velocity for the entire trip?

You drive on Interstate 10 from San Antonio to Houston, half the time at 55 km/h and the other half at 90 km/h. On the way back you travel half the distance at 55 km/h and the other half at 90 km/h. What is your average speed for the entire trip?

A traditional unit of length in Japan is the ken (1 ken = 1.97 m). What are the ratios of square kens to square meters?

At a construction site a pipe wrench struck the ground with a speed of 24 m/s. From what height was it inadvertently dropped?

An electric vehicle starts from rest and accelerates at a rate of $2.0 \textrm{ m/s}^2$ in a straight line until it reaches a speed of $20 \textrm{ m/s}$. The vehicle then slows at a constant rate of $1.0 \textrm{ m/s}^2$ until it stops.

How much time elapses from start to stop?

Find the curvature of the curve y = x^4 at the point (1, 1)

A sound wave travels out uniformly in all directions from a point source. Justify the following expression for the displacement s of the transmitting medium at any distance r from the source:

$${s = {\frac{b}{r}} sin k(r - vt),}$$

where b is a constant.

Adderall is a proprietary combination of amphetamine salts that is used to treat ADHD (Attention Deficit/Hyperactivity Disorder). The patient takes one pill before 8 am, and the drug has completely entered the blood by 8 am. At 8 am the blood concentration of the drug is 33.8 ng/ml. Adderall has first order elimination kinetics with 7.7% of the drug being removed from the blood in each hour. The data in this equation are taken from Greenhill et al. (2003).
(a) The concentration of drug in the patient’s blood t hours after 8 am is measured to be C$_t$ . Write a recursive relation for C$_{t+1}$ in terms of C$_t$ . Assume that the patient takes no other Adderall pills.
(b) Solve your recurrence equation to derive an explicit formula for C$_t$ as a function of t.
(c) When does the concentration of drug first drop below 0.1 ng/ml?

You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (-140 m, 30 m). The x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (b_x and -70), then (-20 and c_y), then (-60 and -70). What are (a) component b_x and (b) component c_y? What are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement?

A person walks in the following pattern: 3.1 km north, then 2.4 km west, and finally 5.2 km south. (a) Sketch the vector diagram that represents this motion. (b) How far and (c) in what direction would a bird fly in a straight line from the same starting point to the same final point?

Determine the color and approximate wavelength absorbed most strongly by each solution. a. blue solution, b. red solution, c. yellow solution.