2. 1D Motion / Kinematics

The figure shows two vectors. Which choice best represents $\stackrel{\rightharpoonup }{A}-\stackrel{\rightharpoonup }{B}$?

Seen from above, Linda runs $5.0\mathrm{m}/\mathrm{s}$ 30° north of east. What is the x component of her velocity?

If $\stackrel{\rightharpoonup }{A}=3\widehat{i}-2\widehat{j}$, $\stackrel{\rightharpoonup }{B}=2\widehat{i}$, and $\stackrel{\rightharpoonup }{C}=2\stackrel{\rightharpoonup }{B}-\stackrel{\rightharpoonup }{A}$, what is $\stackrel{\rightharpoonup }{C}$?

Draw a pictorial representation for the following problem. Do not solve the problem. What acceleration does a rocket need to reach a speed of 200 m/s at a height of 1.0 km?

Problems 49, 50, 51, and 52 show a partial motion diagram. For each: c. Draw a pictorial representation for your problem.

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.

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?

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.

A bowling ball rolls up an incline and then onto a smooth, level surface. Draw a complete motion diagram of the bowling ball. Don't try to find the acceleration vector at the point where the motion changes direction; that's an issue for Chapter 4.

A speed skater accelerates from rest and then keeps skating at a constant speed. Draw a complete motion diagram of the skater.

You drop a soccer ball from your third-story balcony. Use the particle model to draw a motion diagram showing the ball's position and average velocity vectors from the time you release the ball until the instant it touches the ground.

A jet plane lands on the deck of an aircraft carrier and quickly comes to a halt. Draw a basic motion diagram, using the s from the video, from the time the jet touches down until it stops.

You are watching a jet ski race. A racer speeds up from rest to 70 mph in 10 s, then continues at a constant speed. Draw a basic motion diagram of the jet ski, using s from the video, from its start until 10 s after reaching top speed.

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 jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jet's acceleration as it speeds up?

FIGURE EX1.10 shows two dots of a motion diagram and vector . Copy this figure, then add dot 4 and the next velocity vector if the acceleration vector at dot 3 (b) points left.

FIGURE EX1.9 shows five points of a motion diagram. Use Tactics Box 1.2 to find the average acceleration vectors at points 1, 2, and 3. Draw the completed motion diagram showing velocity vectors and acceleration vectors.

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.

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 traveling at 30 m/s runs out of gas while traveling up a 10° slope. How far up the hill will the car coast before starting to roll back down?

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. David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. How far does Tina drive before passing David?

Problems 49, 50, 51, and 52 show a partial motion diagram. For each: a. Complete the motion diagram by adding acceleration vectors.

Problems 49, 50, 51, and 52 show a partial motion diagram. For each: a. Complete the motion diagram by adding acceleration vectors.

Problems 49, 50, 51, and 52 show a partial motion diagram. For each: c. Draw a pictorial representation for your problem.

A steel ball rolls across a 30-cm-wide felt pad, starting from one edge. The ball's speed has dropped to half after traveling 20 cm. Will the ball stop on the felt pad or roll off?

The vertical position of a particle is given by the function y = (t^2 - 4t + 2) m, where t is in s. (b) What is the particle's position at that time?

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

A particle moving along the x-axis has its position described by the function x = (2t^3 + 2t + 1) m, where t is in s. At t = 2s what are the particle's (a) position

A particle's velocity is described by the function vₓ =kt² m/s, where k is a constant and t is in s. The particle's position at t₀ = 0 s is x₀ = ─9.0 m. At t₁ = 3.0 s, the particle is at x₁ = 9.0 m. Determine the value of the constant k. Be sure to include the proper units.

The position of a particle is given by the function x = (2t^3 = 6t^2 + 12) m, where t is in s. (a) At what time does the particle reach its minimum velocity? What is (vx)min?

A particle's velocity is given by the function 𝓋ₓ = (2.0 m/s) sin (πt), where t is in s. a. What is the first time after t = 0 s when the particle reaches a turning point?

A particle moving along the x-axis has its veocity described by the function vx = 2t^2 m/s, where t is in s. itsinitial position is x0 = 1 m at t0 = 0 s. At t = 1 s what are the particle's (a) position

The position of a particle is given by the function x = (2t^3 = 6t^2 + 12) m, where t is in s. (b) At what time is the acceleration zero?

When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 s is extremely well modeled by the simple equation where P = 3.6 ✕ 10⁴ watts is the car's power output, m = 1200 kg is its mass, and v𝓍 is in m/s. That is, the square of the car's velocity increases linearly with time. a. Find an algebraic expression in terms of P, m, and t for the car's acceleration at time t.

CALC. A car's velocity as a function of time is given by v_x(t) = α + βt^2, where α = 3.00 m/s and β = 0.100 m/s^3. (c) Draw v_x-t and a_x-t graphs for the car's motion between t = 0 and t = 5.00 s.

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)t2. (e) Sketch graphs of x versus t, υx versus t, and ax versus t, for the time interval t = 0 to t = 40 s.

A rubber ball bounces. We'd like to understand how the ball bounces. a. A rubber ball has been dropped and is bouncing off the floor. Draw a motion diagram of the ball during the brief time interval that it is in contact with the floor. Show 4 or 5 frames as the ball compresses, then another 4 or 5 frames as it expands. What is the direction of a during each of these parts of the motion?