phy

Displacement from 3 to 6 seconds on the "Oops ... My Hydro" graph

A student is walking as shown by the "Oops ... My Hydro" graph. Determine the magnitude of the student's displacement 3 to 6 seconds. Answer: 9 meters.

Velocity from a position vs time graph

Slope = velocity. The slope of a position versus time graph gives the velocity.

Distance from a velocity vs time graph

Area under a velocity vs time graph = displacement.

Distance traveled during first four seconds on the "Hurry Up!" graph

Using the provided "Hurry Up!" graph, how far did the object travel during the first four seconds? Answer: 9 meters.

Average velocity

Average velocity = total displacement divided by total time.

Scalar Quantity

A scalar quantity has magnitude only and no direction.

Vector Quantity

A vector quantity has both magnitude and direction.

Difference between vectors and scalars

Vector quantities have both magnitude and direction while scalar quantities only have magnitude.

Uniform acceleration time equation

v = vi + at.

Time during acceleration

An athlete is running and accelerates uniformly through the final 25 meters of a race before finishing with a higher speed. The athlete accelerated for 3.91 seconds.

Free fall position equation

y = vit + 1/2at².

Baseball thrown upward problem

An athlete throws a baseball upward with an initial speed of 13 m/s. Once the baseball leaves the player's hand the timer begins. How high above the player's hand is the baseball after 2.0 seconds have elapsed? Answer: 6.4 meters.

Motorcycle slowing to a stop on a position vs time graph

A motorcycle moving with an initial positive velocity before slowing to a stop with a uniform acceleration is represented by a position versus time graph with a decreasing positive slope.

Motorcycle slowing to a stop on a velocity vs time graph

A motorcycle moving with an initial positive velocity before slowing to a stop with a uniform acceleration is represented by a straight line decreasing toward zero on a velocity versus time graph.

Acceleration from velocity and displacement

vf² = vi² + 2ad.

Truck stopping acceleration problem

A truck is driving along a level road at a speed of 33 m/s and comes to a stop in 125 meters. Calculate the acceleration of the truck using vf² = vi² + 2ad.

Acceleration and changing direction

If an object changes direction, then it must be accelerating.

Speed

Speed is a scalar quantity and has magnitude only.

Velocity

Velocity is a vector quantity and has both magnitude and direction.

Same speed but different velocity

Two cars moving at the same speed in opposite directions have the same speed but different velocities.

Object dropped inside moving truck

A truck is moving at constant speed. A caramel apple dropped from the ceiling will land directly below its drop point because the apple and truck move horizontally at the same speed.

Horizontal projectile motion time

Objects launched horizontally from the same height hit the ground at the same time regardless of horizontal speed.

Sphere impact question

Anne launches two spheres horizontally from the same height with different horizontal speeds. Both impact the floor at the same time.

Faster horizontal speed projectile motion

The sphere with the slower horizontal speed lands closer to the platform because both are in the air for the same amount of time.

Newton's Second Law

Fnet = ma.

Bucket acceleration problem

A student pulls upward on a 65 kg bucket with a force of 888 N. Use Fnet = ma to determine the resulting acceleration on the bucket.

Friction force equation

Ff = μFn.

Coefficient of friction problem

A truck skids 57 meters before stopping. The coefficient of friction between the tires and the surface is 0.43.

Newton's Third Law

For every action force there is an equal and opposite reaction force.

Shopping cart collision

Two shopping carts collide. Both carts exert the same force on each other despite the different motions after the collision.

Acceleration of connected masses

a = Fnet / mtotal.

Pulley system problem

A block of mass 3m is attached to a hanging block of mass m over a pulley. Both masses accelerate together so the total mass must be added.

Normal force on an incline

Fn = mg cos(θ).

Ramp normal force problem

A 10 kg block slides at constant velocity down a 20 degree ramp. The normal force is 92 N.

Friction force on an incline

Ff = mg sin(θ).

Constant velocity forces

If an object moves with constant velocity, the forces are balanced and the net force is zero.

Centripetal force direction

Centripetal force always points toward the center of the circle.

Tangent motion after string breaks

If a string breaks during circular motion, the object moves tangent to the circular path.

Circumference of a circle

C = 2πr.

Equal radius circular motion

Two objects moving in circles with the same radius have the same circumference.

Velocity in circular motion

v = 2πr / T.

Equal velocity circular motion

Two objects with the same radius and period have the same velocity.

Centripetal force equation

Fc = mv² / r.

Greater centripetal force

If two objects move with the same speed and radius but one has greater mass, the more massive object has the greater centripetal force.

Universal gravitation equation

Fg = Gm1m2 / r².

Gravitational force and distance

Increasing the distance between two masses decreases the gravitational force.

Keeping gravitational force constant

If the distance between two masses doubles, both masses must also double to keep the same gravitational force.

Elastic potential energy equation

PEelastic = 1/2kx².

Spring constant problem

A horizontal spring is compressed 0.3048 meters and stores 1.25 Joules of elastic potential energy. Use PEelastic = 1/2kx² to calculate the spring constant.

Gravitational potential energy equation

PEg = mgh.

Trampoline energy problem

A 65 kg student reaches a height of 2.75 meters above a trampoline. The trampoline transfers 1750 Joules of energy to the student.

Kinetic energy equation

KE = 1/2mv².

Student speed above trampoline

A student descending to 1 meter above the trampoline is traveling at the speed found using conservation of energy.

Power equation

P = W/t.

Crane gravitational potential energy problem

A crane lifts an 85 kg statue headpiece 15 meters. The change in gravitational potential energy is 12495 Joules.

Crane power problem

A crane lifts an 85 kg statue headpiece 15 meters in 30 seconds. The power required is 417 Watts.

Conservation of energy

Initial energy = final energy + energy lost.

Car traveling up hill energy problem

A car travels up a hill while resistive forces remove energy from the car. Use conservation of energy to determine the height of the hill.

Distance from velocity vs time graph

The area under the line on a velocity versus time graph equals the total distance traveled.

Net force during braking

Fnet = ma. Use acceleration during braking to calculate the net force on the car.

Circular motion period equation

T = 2πr / v.

Decreasing circular motion period

Decreasing the radius decreases the period because the object travels a shorter distance each rotation.

Mass and circular motion period

Decreasing the mass decreases the period because a smaller mass experiences greater centripetal acceleration for the same force.