2. 1D Motion / Kinematics

A good model for the acceleration of a car trying to reach top speed in the least amount of time is a_x = a₀ ─ kv_x, where a₀ is the initial acceleration and k is a constant. Find an expression for k in terms of a₀ and the car's top speed v_max.

Which of the following best describes $d$isplacement, given that it has both magnitude and direction?

Which of the following best explains how $velocity$ differs from $speed$, and why $velocity$ is considered a $vector$ quantity?

If east is the reference direction, then a train that is $-10m$ from you is toward the:

Your roommate drops a tennis ball from a third-story balcony. It hits the sidewalk and bounces as high as the second story. Draw a complete motion diagram of the tennis ball from the time it is released until it reaches the maximum height on its bounce. Be sure to determine and show the acceleration at the lowest point.

Given the following quantities, select the correct description for each: (A) $v$, (B) $d$, (C) $t$, (D) $m$. Which option correctly matches each symbol to its physical quantity? (A) velocity, (B) displacement, (C) time, (D) mass.

In physics, what type of quantity is $distance$ considered to be?

Which of the following vectors represents the resultant of adding vectors $a$ and $b$?

For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics. A car starts from rest at a stop sign. It accelerates at 4.0 m/s² for 6.0 s, coasts for 2.0 s, and then slows at a rate of 2.5 m/s² for the next stop sign. How far apart are the stop signs?

A turtle crawls along a straight line, which we will call the $x$-axis with the positive direction to the right. The equation for the turtle's position as a function of time is $x(t) = 50.0$ cm + ($2.00$ cm/s)$$$t$ − ($0.0625$ cm/s²)$t^2$. Sketch graphs of $x$ versus $t$, $v_x$ versus $t$, and $a_x$ versus $t$, for the time interval $t=0$ to $t=40$ s.

FIGURE EX1.8 shows the first three points of a motion diagram. Is the object's average speed between points 1 and 2 greater than, less than, or equal to its average speed between points 0 and 1? Explain how you can tell.

The position of a particle is given by the function x = (2t³ = 6t² + 12) m, where t is in s. At what time does the particle reach its minimum velocity? What is (v_x)_min?

Problems 44, 45, 46, 47, and 48 show a motion diagram. For each of these problems, write a one or two sentence 'story' about a real object that has this motion diagram. Your stories should talk about people or objects by name and say what they are doing.