Essential Physics Concepts: Kinematics, Dynamics, and Projectile Motion

Fundamental Concepts in Kinematics and Dynamics

I. Dynamics and Forces

Impulse and Time Interval

If the force exerted on a car is halved, the required time interval to achieve the same impulse must be: Twice as long

Impulse and Mass

If a heavier cart (double the mass) receives the same impulse as a lighter cart, its final speed relative to the lighter cart is: Half

Normal Force in an Elevator

When an elevator accelerates upward, the upward normal force (N) exerted by the floor is: Larger

Net Force During Curving Motion

Is there a net force on the car as it rounds the curve? No, constant (Note: This answer implies constant speed, but a net centripetal force is required.)

Newton's Third Law Application

Consider a horse pulling a buggy: Yes (Interaction forces exist)

Non-Newtonian Concepts

Which concept is not one of Newton’s Laws? Absolute friction

Definition of Normal Force

The force that is perpendicular to the surface of contact is called the: Normal Force

Acceleration Due to Gravity

If two balls of the same size but different weights are dropped simultaneously (ignoring air resistance), their acceleration is the: Same

II. Kinematics: Velocity and Acceleration

Initial Acceleration Upon Release

You hold a ball in your hand at a fixed height and release it. What is the direction of its initial acceleration? Down

Symmetry of Vertical Motion

A bullet is fired straight up from height H. If it returns to height H, how does its speed compare to the initial speed (ignoring air resistance)? Same

Time Symmetry in Vertical Motion

If an object is thrown upward past a window, the time taken to travel up ($t_u$) compared to the time taken to travel down ($t_d$) is: $t_u = t_d$

Motion at the Highest Point

If a ball is thrown upwards, at the highest point: Velocity ($v$) is zero, acceleration ($a$) is not equal to zero

Simultaneous Zero Velocity and Non-Zero Acceleration

Can $v = 0$ and $a eq 0$ occur simultaneously? Yes

Simultaneous Zero Acceleration and Non-Zero Velocity

Can $a = 0$ and $v eq 0$ occur simultaneously? Yes

Distance vs. Displacement

How does the magnitude of the displacement compare to the total distance traveled when an object goes from one point in space to another? Either smaller than or equal to

Definition of Acceleration

Acceleration is: A change in velocity

Uniform Acceleration

Motion is uniformly accelerated when: Acceleration is constant

Speeding Up or Slowing Down

An object has a negative velocity and a negative acceleration. It is: Speeding up

Acceleration and Constant Velocity

Is it possible for an object to be accelerating while traveling at constant velocity? False (F)

Highest Point Kinematics

A ball is thrown straight up in the air. At the highest point: Acceleration ($a$) is non-zero, velocity ($v$) is zero.

True/False Statements on Kinematics

• Constant velocity means that the acceleration is zero. True (T)
• Constant acceleration means that the acceleration is zero. True (T)
• Acceleration can be negative. True (T)
• Velocity can be negative. True (T)
• Displacement can be negative. True (T)
• The negative sign of the acceleration always means the object is slowing down. False (F)
• If an object’s velocity is zero, its acceleration must also be zero. False (F)
• Positive acceleration always means the object is speeding up. False (F)

III. Projectile Motion Analysis

Projectile Motion Characteristics

A projectile thrown at an angle has a: Uniform horizontal velocity and changing vertical velocity (uniform h-v)

Horizontal Acceleration

In ideal projectile motion, the horizontal component of acceleration is zero. True (T)

Vertical Acceleration

In ideal projectile motion, the vertical component of acceleration is zero. False (F)

Horizontal Distance Covered

A projectile covers equal horizontal distances in equal time intervals. True (T)

Constant Velocity Components

Do both the horizontal and vertical components of the velocity remain constant during projectile motion? False (F)

Launch and Landing Speed Symmetry

If launched at 20 m/s from level ground, the magnitude of its velocity before striking the ground is 20 m/s. True (T)

Maximum Range Angle

The launch angle (like from a garden hose) that maximizes horizontal range is: 45 degrees

Minimum Speed Point

At what part of its trajectory does a projectile have minimum speed? The top (highest point)

Horizontal Acceleration Value

What is the horizontal acceleration ($a_x$) in ideal projectile motion? Zero ($a_x=0$)

Symmetry Properties

For a projectile that goes up and down to the same height, symmetry applies to speed, angle, and time: All

Deviation from Ideal Path

What factor deviates the path of a projectile from its ideal parabolic behavior? Air resistance

Initial Vertical Velocity (Horizontal Launch)

If a ball is thrown horizontally at 10 m/s, the vertical component of the initial velocity ($v_{iy}$) is: 0 m/s

Initial Horizontal Velocity (Horizontal Launch)

If a ball is thrown horizontally at 10 m/s, the horizontal component of the initial velocity ($v_{ix}$) is: 10 m/s

Zero Vertical Velocity Point

The vertical component of the velocity will be zero when the projectile reaches: The highest point