2. 1D Motion / Kinematics

Which of the following is a pair of vector quantities?

Starting from a pillar, you run a distance 140m east (the + x-direction), then turn around. 

(a) How far west would you have to walk so that your total distance traveled is 300m?

(b) What is the magnitude and direction of your total displacement?

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.

If a vector lies in the first quadrant of a standard Cartesian coordinate system and motion is along a straight path, which of the following conditions will result in both components of the vector being positive?

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 EX1.9 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.

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?

A force of magnitude $10$ $N$ acts at an angle of $30°$ above the positive $x$-axis in the $xy$-plane. How can this force be expressed as a Cartesian vector?

A person walks $4$ km east and then $3$ km north. What is the magnitude of the resultant displacement from the starting point?

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are vectors, what is the magnitude of $\overrightarrow{b}-3\overrightarrow{a}$ in terms of the magnitudes of $\overrightarrow{a}$ and $\overrightarrow{b}$, assuming they are in the same direction?

Why is $d$istance alone insufficient to determine an object's location relative to another object?

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.