Mechanics 1

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Questions and Answers

A car accelerates uniformly from rest at $3 \text{ m/s}^2$. How far does it travel in $4$ seconds?

  • $18 \text{ m}$
  • $36 \text{ m}$
  • $12 \text{ m}$
  • $24 \text{ m}$ (correct)

Instantaneous speed is defined as the total distance traveled divided by the total time elapsed.

False (B)

A train travels at a constant velocity of $20 \text{ m/s}$ for $10$ seconds. What is the displacement during this time?

$200 \text{ m}$

An object thrown upwards with an initial velocity of $v_i$ experiences a downward acceleration due to gravity, approximately equal to _______.

<p>$9.8 \text{ m/s}^2$</p> Signup and view all the answers

Match each kinematic term with its corresponding definition:

<p>Displacement = Change in position with direction Velocity = Rate of change of displacement Acceleration = Rate of change of velocity Speed = Rate of change of distance</p> Signup and view all the answers

An object is dropped from a height of $45 \text{ m}$. Assuming no air resistance, how long does it take to reach the ground? (Use $g = 10 \text{ m/s}^2$)

<p>$3 \text{ s}$ (B)</p> Signup and view all the answers

Deceleration always implies that an object is slowing down, regardless of its direction of motion.

<p>False (B)</p> Signup and view all the answers

A car's velocity changes from $10 \text{ m/s}$ to $25 \text{ m/s}$ over a period of $5$ seconds. Calculate the average acceleration.

<p>$3 \text{ m/s}^2$</p> Signup and view all the answers

For an object undergoing uniform acceleration, the average speed is equal to _______ during the time interval.

<p>$\frac{v_f + v_i}{2}$</p> Signup and view all the answers

A plane flies at $100 \text{ km/h}$ in still air, and there is a wind of $30 \text{ km/h}$ in the opposite direction. What is the resultant speed of the plane?

<p>$70 \text{ km/h}$ (D)</p> Signup and view all the answers

Flashcards

What is Mechanics?

Study of motion. What causes motion and how it changes.

What is Kinematics?

The branch of mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move.

What is Speed?

The rate of change of position of an object in a given time.

What is Average Speed?

The total distance traveled divided by the total time it takes.

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What is Instantaneous Speed?

The speed of an object at a particular time.

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What is Acceleration?

The rate of change of the speed.

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What is Displacement?

Displacement describes distance and direction to the object.

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What is Velocity?

Rate of change of the displacement.

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What is Deceleration?

Acceleration in the opposite direction to the velocity vector.

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What is Acceleration due to Gravity?

All objects falling freely towards Earth have the same acceleration; ≈ 10 m/s².

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Study Notes

  • Mechanics involves the study of motion and its causes.

Relevance Demonstrated Through Exam Question

  • A question from a 2005 physics final exam highlights the importance of understanding mechanics.
  • The problem involves two cars, one moving at a constant velocity and the other accelerating.
  • The question asks for the speed of the accelerating car when it passes the car moving at a constant speed.
  • Less than 50% of students answered correctly.

Kinematics Learning Goals

  • Kinematics is the description of motion, and why it's important in physics.
  • Fundamental kinematic quantities are time, distance, speed, and acceleration.
  • Vector quantities include displacement, velocity, and acceleration.
  • Kinematics also covers average and instantaneous quantities.
  • Relative displacement, velocity, and acceleration are part of kinematics.

Understanding Motion

  • Quantities are needed to describe motion adequately.
  • Motion involves a change in position with time.
  • Time and position must be measured to analyze motion.
  • Rates of change, including position and the rate of change of the rate of change, are important.

Time, Distance, and Speed Defined

  • Calculating distance traveled over time by an object.
  • A car moving at 5 m/s travels 15 meters in 3 seconds.
  • Speed is the rate of change of an object's position over time, expressed as v = Δx/Δt, where Δ means "change in."
  • To find the distance traveled at a constant speed, use Δx = vΔt.
  • For a car traveling at 5 m/s for 3 seconds, the distance covered (Δx) is 15 meters.

Average Speed Explained

  • Average speed is total distance traveled divided by total time.
  • Average speed is expressed as V(av) = Δx/Δt.
  • Average speed is not the speed at a particular time.
  • At constant acceleration, average speed = (V(f) + V(i)) / 2.

Instantaneous Speed Defined

  • Instantaneous speed is the speed of an object at a particular moment.
  • As Δx and Δt decrease, average speed approaches instantaneous speed.

Example of Average Speed

  • Driving 300 km to Christchurch in 5 hours results in an average speed of 60 km/h.
  • The instantaneous speed varies during the trip.

Understanding Acceleration

  • Acceleration is the rate of change of speed.
  • Acceleration is expressed as a = Δv/Δt.
  • The change in speed for a given uniform acceleration is found using Δv = aΔt.
  • A car accelerating from rest at 2 m/s² for 4 seconds will have a final speed of 8 m/s.

Train Speed Example

  • A train's speed increases uniformly from 3 m/s to 11 m/s over 100 seconds, resulting in an average speed of 7 m/s.
  • The equation provides the average speed, V(av) = (V(f) + V(i)) / 2.
  • The train travels 700 meters in 100 seconds (Δx = V(av)Δt).

Uniform Acceleration Detailed

  • For an object with uniform acceleration, Δx = V(av)Δt.
  • Δx = 1/2 * (Vi + Vf) * Δt which can be expressed as Δx = ViΔt + 1/2 aΔt².
  • If the object starts from rest, Δx = 1/2 aΔt².

Vector Quantities Specified

  • Displacement: Vector describing distance and direction to an object, exemplified by "3 m north" or "4 m east."
  • Velocity: Rate of change of displacement, illustrated by "12 km/h south" or "10 m/s NE."
  • Acceleration: Rate of change of velocity.
  • Deceleration: Acceleration opposing the velocity vector.

Adding Velocities: Understanding Relative Motion

  • When an airplane flies at 100 km/h in still air with a 30 km/h wind, its speed relative to the ground changes.
  • If the wind is in the same direction, the resultant speed is 130 km/h.
  • If the wind is in the opposite direction, the resultant speed is 70 km/h.
  • A bird flying north at 3 m/s with a 4 m/s easterly wind has a resultant velocity of 5 m/s at 37° N of E.

Acceleration Due to Gravity

  • Galileo discovered objects falling freely towards Earth accelerate equally, a = g = 9.8 m/s² ≈ 10 m/s².
  • 'g' signifies acceleration due to gravity.
  • Velocity changes by Δv = gΔt under gravity.
  • After 5 seconds of free fall from rest, Δv = 10 m/s² * 5 s = 50 m/s.

Free Fall Calculations

  • A cricket ball dropped from a plane falls 125 m in 5 seconds.
  • Uses formulas for constant acceleration to determine free fall distance.

Projectile Motion Explained

  • A cricket ball thrown upwards at 30 m/s will reach a height of 45 meters.
  • Formulas used are Vf = Vi + aΔt, Δx = V(av)t.
  • Takes 3 seconds to reach max height.

Example of Time to Reach the Ground

  • The ball takes same time (3 s) to come down as to go up.
  • Starts with Vi=0, Δx=45 m, g=10 m/s using the formula Δx = (1/2)gΔt².
  • Downward velocity at ground is the same as the launch (30m/s).

Vertical and Horizontal Motion

  • Vertical and horizontal motions are considered independent.
  • Objects fall at the same rate.

Ball Flight Trajectory

  • If horizontal velocity = 10 ms-1, and the flight is independent, then a parabolic motion occurs.

Relative Motion

  • A polar bear is 200m behind a man running at 7 m/s.
  • The polar bear is running at 11 m/s to the man's car.
  • The bear's velocity relative to the man is 4 m/s.
  • It will take the bear 50secs to catch the man.

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