Browse Problems
54 problems tagged with linear motion
P0283
Intermediate Mechanics › KinematicsRelative Motion Analysis of Two Cars
Car A starts at position $x_{A0}$ with a constant velocity $v_A$. Car B starts at the origin with an initial velocity $v_{B0}$ and a constant negative acceleration $a_B$. Assume $v_{B0} > v_A > 0$ and $x_{A0} > 0$.
- What must $a_B$ be such that the cars are at the same position at time $t_1 > 0$?
- For this acceleration, what is the other time $t_2$ when the cars are at the same position?
- Find the critical magnitude of acceleration, $A_{crit} = |a_B|_{crit}$, for which the cars meet only once.
- For $A = |a_B|$, how many times do the cars meet if $A > A_{crit}$ or if $A < A_{crit}$?
P0268
Beginner Mechanics › KinematicsAirplane Landing Deceleration and Position
An airplane lands with an initial velocity of 60 m/s and decelerates uniformly at a rate of 6 m/s².
P0271
Intermediate Mechanics › KinematicsKinematic Analysis of Two Moving Objects
Two objects, A and B, are in motion. Their displacements as a function of time are given by the equations $s_A = 4t^2 + 2t$ and $s_B = 8t - 0.8t^2$. The unit for displacement is meters (m) and for time is seconds (s).
- Describe the type of motion for each object and write their respective velocity-time equations.
- At what time are the velocities of the two objects equal?
P0264
Beginner Mechanics › KinematicsUniformly Accelerated Linear Motion Calculation
An object undergoes uniformly accelerated linear motion. It travels a distance of 255 m in 30 s. At the end of the 30 s interval, its velocity is 16 m/s.
- Find the object's acceleration.
- Find the object's initial velocity.
P0267
Beginner Mechanics › KinematicsObject Dropped from a Rising Balloon
An object is dropped from a hot air balloon when the balloon is at a height of 150 m above the ground. The object takes 6 s to reach the ground. Assume the acceleration due to gravity is $g = 10 \text{ m/s}^2$.
P0243
Beginner Mechanics › KinematicsAnalysis of a Vertical Water Jet
A fire hose ejects water at a flow rate of 280 L/min and an initial speed of 26 m/s. The water is sprayed vertically upwards. Air resistance is negligible and Earth's gravity is $g = 9.8$ m/s².
- What is the maximum height the water stream can reach?
- At any given moment, how many liters of water are in the air?
P0001
Beginner Mechanics › KinematicsHeight of a Balloon Releasing an Object
An object is dropped from a balloon that is ascending at a constant velocity of 8 m/s. The object takes 3 s to reach the ground after being released.
P0266
Beginner Mechanics › KinematicsFreely Falling Ball Passing Two Points
A ball is in free fall. It passes point A with a velocity of 20 m/s and then point B with a velocity of 25 m/s. After passing point B, it takes an additional 0.5 s to reach the ground. Assume $g = 10 \text{ m/s}^2$.
- Find the distance between points A and B.
- Find the initial height from which the ball was dropped.
P0214
Beginner Mechanics › KinematicsAverage Speed Over Two Halves of a Journey
An object undergoes variable speed motion. Its average speed in the first half of the journey is 3 m/s, and its average speed in the second half of the journey is 5 m/s.
P0215
Beginner Mechanics › KinematicsDisplacement in Uniformly Accelerated Motion
An object starts from rest and undergoes uniformly accelerated linear motion. When its velocity is $v$, its displacement is $s$.
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