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Practice: Drone flight

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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

One-Dimensional Kinematic Equations

3 Activities

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
III. After rising for 20  m20\;m, it suddenly changed its vertical velocity to 12 m/s12\ m/s
IV. When it reached the height of 100 m100\ m above the ground it accelerates downward with magnitude of 1m/s21 m/s^2
V. It got back to the ground level

a) At what time did the drone rise its speed to 12 m/s12\ m/s?
b) At what time did the drone reach to 100 m100\ maltitude?
c) At what time was the drone’s velocity changed direction from upward to downward and what was the altitude at that moment?
d) At what time did the drone get back to the ground?
e) Sketch yyvs tt graph of the drone's motion.
f) Sketch vyv_yvs tt graph for the drone's motion.
a) At what time did the drone rise its speed to 12 m/s12\ m/s?
More Kinematic Graphs Questions:
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.
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?
More One-Dimensional Kinematic Equations Questions:
Dave drives a truck at a constant 20 m/s and passes me on my stationary motorbike, at which point I lay on the gas and accelerate at 8.0 m/s2. How far has my motorbike driven when I pass Dave?
Motion in 1D and Acceleration
A car is travelling at 20 m/s and the driver applied the brake for 10 seconds before the car comes to a stop.
Kinematics
Your dog, Buttercup, sees your neighbour's cat (Waffles) running at its maximum speed of 4 m/s4\ m/s. If your dog can go from 0 to 60 km/h in a time of 15 seconds, will Buttercup catch Waffles before the 35m35mdriveway ends? Show your work.
Kinematics
A bike speeds up from 10.0km/hr10.0 km/hrto 32.0km/hr32.0 km/hrin 15.0s15.0 s. The acceleration is constant.
a) What is the acceleration of the bike? Enter your answer in m/s2.
b) How much distance was traveled in that time? Enter your answer in meters.
Kinematics: Braking Distance
A car can decelerate at 4.0 m/s2m/s^2. If somebody is driving this car at 110 km/h and human reaction time is 0.45 seconds, what will the stopping distance be for the driver?
Using the equations and problem-solving steps: Police chase
Let's illustrate the use of kinematic equations and problem-solving steps with an example.
A vehicle travelling 130 km/h passes a police car at rest. As soon as the vehicle passes the police car, the police car turns its lights on and begins to accelerate to its maximum speed of 140 km/h.
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
A car is travelling at 20 m/s and the driver applied the brake for 10 seconds before the car comes to a stop.
A block is sliding on gym floor. The coefficient of static and kinetic friction between the block and the floor are 0.40.4and 0.070.07 respectively. If the block is initially traveling at 3 m/s3\ m/s find the total distance the block must travel to stop. Draw and label a FBD for both the initial state and the final state.
If a bullet leaves the muzzle of a rifle at 600.0 m/s, and the barrel is 0.90 m long, what was the acceleration of the bullet while in the barrel?
Enter your answer in scientific notation in the following form: 1.0x10^2. Don't include units in your answer (units are in m/s2)
Practice question: kinematic equations
A bullet is fired through a board 10.0 cm thick in such a way that the bullet’s line of motion is perpendicular to face of the board. If the initial speed of the bullet is 400 m/s and it emerges from the other side of the board with a speed of 300 m/s, find (a) the acceleration of the bullet as it passes through the board and (b) the total time the bullet is in contact with the board.
A ball is thrown with an initial upwards velocity of v0v_0from a height hh(both of these values are positive).
a) What is the maximum velocity during the motion?
b) What is the point of minimum acceleration?
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
Your dog Buttercup sees your neighbour's cat (Mr. Waffles) running past at its top speed of 4 m/s4\ m/s. If your dog has an impressive 0−60 km/h0-60\ km/hof 15s15 swill Buttercup catch Mr. Waffles before the 35m35mdriveway ends?
Two runners (Bob and Alice) are racing. Alice is much faster than Bob and is placed such that she starts 25 m25\ m behind Bob. She is 1.51.5 times 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\ m race if Alice has to start 200 m200\ m behind?
A bike accelerates constantly from 10km/hr10km/hr to 32km/hr32km/hr in 15s15 s. What is the acceleration of the bike? How much distance was traveled in that time?
Dave drives a truck at a constant 20 m/s and passes me on my stationary motorbike, at which point I lay on the gas and accelerate at 8.0 m/s2. How far has my motorbike driven when I pass Dave?
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? How long until it stops? What is the box's total displacement?
Kinematic equations
If a bullet leaves the muzzle of a rifle at 600.0 m/s, and the barrel is 0.90 m long, what was the acceleration of the bullet while in the barrel?
Enter answer in m/s2
Practice question: kinematic equations
A bullet is fired through a board 10.0 cm thick in such a way that the bullet’s line of motion is perpendicular to face of the board. If the initial speed of the bullet is 400 m/s and it emerges from the other side of the board with a speed of 300 m/s, find:
(a) the acceleration (in km/s2 ) of the bullet as it passes through the board and
(b) the total time (in sec) the bullet is in contact with the board.
A speeding car is traveling at a constant 50 m/s when it passes a stationary police car. If the police car delays 2s before starting, what must be the magnitude of the constant acceleration of the police car to catch the speeding car after the police car travels a distance of 500 m?
A car is travelling at 20m/s and the driver applied the brake for 10 seconds before the car comes to a stop. What is the net acceleration (deceleration) of the car?