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Vanessa is making her way downtown, moving quite fast. She's racing Adam who's …

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

Kinematic Graphs

4 Activities

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

Basic Concepts of Kinematics

5 Activities

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?

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?
Kinematics
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?
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.
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?
More Basic Concepts of Kinematics Questions:
If you walked 3.00km West, and then 5.00km South to get to the store, what angle are you traveling at relative to the South direction? What is the magnitude of your displacement?
If you walked 3.00km West, and then 5.00km South to get to the store, what angle are you traveling at relative to the South direction? What is the magnitude of your displacement?
Practice question: position, velocity, and acceleration
The position of a particle is given by
r⃗(t)=(10t+t2+7)m\vec{r}(t)=(10t+t^2+7)m
a) Calculate instantaneous velocity at t =5 sec
Practice question: position, velocity, and acceleration
The position of a particle is given by
r⃗(t)=10t+t2+7\vec{r}(t)=10t+t^2+7
Calculate instantaneous velocity at t =5 sec, average velocity for interval (3-5 sec). Also calculate instantaneous acceleration at t =1 sec.
Forces: Friction
A professional mover drags a 20kg mattress across the floor. The mover exerts a force of 50 N at 30° to the horizontal. The coefficient of kinetic friction is 0.100. What is the acceleration of the mattress?
I'm moving and packed all my books into a box that weighs 17kg. I pull the box on a weightless dolly with a force of 60N at an angle of 30° to the horizontal surface.
a) What is the acceleration of the box?
b) The box feels the normal force from the ground and the force of gravity. Are the normal force and gravity an action-reaction pair? Explain your answer!
Practice: Distance and Displacement
You drive 200 kilometres west to get from Montreal to Ottawa. On the way back to Montreal, you run out of gas after driving 50 kilometres.
Two runners (Bob and Alice) are racing. Alice is much faster than Bob and is placed such that she starts 25 m25\ mbehind Bob. She is 1.51.5times faster than Bob who runs at 8 m/s8\ m/s.
a) If they both start at the same time, when are these runners at the same point on the track?
b) Who will win in a 1000 m1000\ mrace if Alice has to start 200 m200\ mbehind? Explain your answer.
Throwing a rock down a well
Joe throws a rock straight down a well. He throws it at 13.0m/s, and the well is 5.10m deep. What is the velocity of the rock when it gets to the bottom? Use the conventional coordinates, where up is positive.
Franklin is coming over to your house. He first travels at 3m/s East, and then he travels 3m/s South. What direction is his average acceleration?
In horse racing, units of "horses" are used to measure length. It is defined as the length of a horse, or 8ft. And there are 3.28ft in 1m.
In the 1973 Belmont race, the horse Secretariat (great movie) won by 31 horse lengths. What is that distance in cm?
Riding a ferris wheel
Joanne is riding a ferris wheel that is 100.0m in diametre. Starting at the bottom, she rides 2 and 3/4 revolutions before the wheel gets stuck.
If you walked 3.00km West, and then 5.00km South to get to the store, what angle are you traveling at relative to the South direction? What is the magnitude of your displacement?
A rabbit, escaping a fox, runs 40o north of west at 10.0m/s. A coordinate system is established with the positive x-axis to the east and the positive y-axis to the north. Write the rabbit’s velocity in terms of components and unit vectors.
Taron is off on a rocket. He starts off at Earth, and launches off at 9am. He flies up 200km by 10am, and then another 150km by noon. He returns to Earth at 1:30pm. Give all answers in SI units.
(NB: the video says the trip ends at 2:30pm, this is incorrect. Should be 1:30pm, and the mathematics is still fine.)
a) What was his average speed for the whole trip?
Average acceleration of runner
Frank is running at 3.0m/s. He accelerates until he is travelling at -1.3m/s. What is his average acceleration if it took him 12.0s to do this?
A bird flew 100m to the east then 200m to the northwest. Use the algebraic addition of vectors to find the bird’s net displacement.
A 20.0kg cart is moving at 10.0m/s before it goes down a hill. It ends up 2.0m below where it started, and travelled a distance of 15.0m. What is the speed of the car? There is friction, and it applies an average force of 2.00N over the course of it's motion.
Give your answer in m/s.
I over-packed a box and it weighs 50kg. I'm pulling it across a rough surface at an angle of 45 degrees above the horizontal with a force of 280N. The coefficient of kinetic friction of the floor is 0.5. I pull for 10 seconds, the box speeds up from rest, I release it and it continues to slide to a halt. What is its maximum speed?
Area under plot for displacement
Alice and Bob are having a race. Alice starts off strong, at 10.0m/s, while Bob struggles at 5.0m/s. But 5 minutes later, Alice starts to tire out, and slows to 2.0m/s. Bob sees his chance, and starts running at 7.0m/s. The race ends another 5 minutes later. Who travelled the furthest, winning the race?
Direction of acceleration
Joe is running from 20m to 10m, while he is slowing down. What direction is his acceleration?
If you walk around a circle of diameter of 10 m for π rad, how far have you walked?
Enter answer in meters.
Kinematics question
The slope of position-time graph gives
average velocity
Practice question: position, velocity, and acceleration
The position of a particle is given by
r⃗(t)=10t+t2+7\vec{r}(t)=10t+t^2+7
Calculate instantaneous velocity at t =5 sec, average velocity for interval (3-5 sec). Also calculate instantaneous acceleration at t =1 sec.
A 200g mass block is released from rest at a height of 25 cm on 30o incline. The incline is frictionless. It slides down the incline and then a frictionless surface until it collides elastically with an 800g block at rest 1.4 m from the bottom of the incline as shown in the figure. How much later do the two blocks collide again?
If the velocity of particle is non-zero. Can acceleration of particle be zero?
If the average velocity of an object is zero in some time interval, object's displacement is
zero
The position of a particle of mass 2g is given by r⃗=−3t2i^+2tj^+5k^\vec{r} = -3t^2\hat{i}+2t\hat{j}+5\hat{k} (t is in sec and r is in m).
The magnitude of instantaneous velocity and the magnitude of instantaneous acceleration at t = 3s are:
Practice question: position, velocity, and acceleration
The position of a particle is given by r⃗(t)=(10t+t2+7)m\vec{r}(t)=(10t+t^2+7)m
a) Calculate instantaneous velocity at t =5 sec
b) Calculate the average velocity for an interval (3-5 sec).