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Kinematics

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Wize University Physics Textbook (Master) > Motion in 1/2/3D: Kinematics

Kinematic Graphs

4 Activities

A ball moves according to the following v-t graph. (The graph ends at t=110s.)

a) Find the final displacement of the object.
b) At t=70st=70s which way is the ball traveling?
c) At t=95st=95s which way is the ball traveling?
d) Find the average speed of the object.
e) Find the average velocity of the object. (Positive velocity indicates moving forwards; negative velocity indicates moving backwards.)
f) Are your answers to (d) and (e) the same? Why or why not?


Part (a):
More Kinematic Graphs Questions:
Practice: Drone flight
A drone was controlled as follows:
I. At t=0 st=0\ s, the drone was stationary on the surface of the ground (y=0y=0)
II. At t=5 st=5\ s, it was raised up at a constant speed of 4 m/s4\ m/s
Kinematics
a) Calculate the final velocity in m/sm/s of the car given the following displacement-time graph.
b) What is the maximum velocity, and when does it occur?
c) What is the minimum velocity, and when does it occur?
Practice: Going for a Jog
Your friend went for a jog, and you are looking at their speed measurements against time recorded to their fitness app. Assume that they ran in a single direction (i.e. the direction of the velocity vector is constant).
Practice: Kinematics plots
Consider the motion of the following object. The position and time at each second from t=0 to t=10s are shown both in a table and in a graph, below.
xt00−51−52−153−20405406457458259010\begin{array}{|r|c|}x & t\\0 & 0\\-5& 1\\-5& 2\\-15 & 3\\-20 & 4\\0&5\\40&6\\45&7\\45&8\\25&9\\0&10 \end{array}
Fastest points on plot
Which of the following statements are true at the times (1s, 2s, 3s, 4s)?
What is the total Δy\Delta y from x = 2 to 8?
Sketch the derivative of the following graph
Linearise this!
Given this equation
X5 = 23Y3Z7X^5\ =\ \sqrt{\frac{23Y^3}{Z^7}}
Which of the following plots would be linear?
Proportionality
Given the following equation
X=6YZ4X = \frac{6 \sqrt{Y}}{Z^4}
Which plots will give you a straight line?
Proportionality sketches
Match the following plot sketches with the proportionalities.
Drop the ball
So let's consider a ball that is dropped, starting above the ground, bouncing off the ground and reaching half the original height. And then have the ball fall back to the ground again. Sketch the position/velocity/acceleration graphs.
Vanessa is making her way downtown, moving quite fast. She's racing Adam who's in a big yellow taxi. Their velocities are shown below
Over the entire race, who travelled the longest distance? Who has the greater displacement?
Draw out plot
A driver is traveling at 2.0m/s, and then slows down to a stop at a constant rate in 2.0s. Then he starts accelerating again at 1.5m/s2 for 3.0s.
Draw out the velocity/acceleration-time graphs for the motion.
Instantaneous and average velocity
With the following position-time plot, you can get the average and instanteous velocities. Are the following statements true or false?
Integral of v-t graph
Given the following velocity-time graph
Rank, from lowest to greatest, the velocities at each of the points (v⃗a,v⃗b,v⃗c,v⃗d\vec{v}_a, \vec{v}_b, \vec{v}_c, \vec{v}_d). Then rank, from lowest to greatest, the speeds at each point (va,vb,vc,vdv_a, v_b, v_c, v_d).
Sketch the position-time and acceleration-time graphs for the following motion.
Velocity from acceleration-time plot
Given the following acceleration-time plot, which velocity-time plot is possible?
Fastest points on plot
Which of the following statements of the speeds at the times (1s, 2s, 3s, 4s) is correct?
Linearise
Which plot would give a linear line?
X=12Y3Z2X=\frac{12Y^3}{Z^2}
Practice: Kinematic Graph
draw velocity-time graph corresponding to given position-time graph.
Practice: Acceleration
A drone was controlled as follows:
I. At t=0 st=0\ s, the drone was stationary on the surface of the ground (y=0y=0)
II. At t=5 st=5\ s, it started to raise up at a constant speed of 4 m/s4\ m/s
Calculate the final velocity (in m/sm/s) of the car given the following displacement-time graph. Find the maximum and minimum velocities and when they occur.
A ball moves according to the following v-t graph.
a) Find the final displacement of the object.
b) At t=70st=70swhich way is the ball traveling?