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Where are we now and where might we be going - Types of motion

Grade 7IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Motion is defined as the change in position of an object over time relative to a reference point. If the position of an object does not change with respect to its surroundings, it is said to be at rest.

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Rectilinear Motion: This occurs when an object moves along a straight line. An example is a car traveling on a straight highway or a sprinter running a 100 m100\ m dash.

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Circular Motion: This involves an object moving along a circular path. The distance from the center of the path remains constant. Examples include a stone tied to a string being whirled around or a satellite orbiting a planet.

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Rotational Motion: This is the motion of an object around a fixed axis passing through its own body. Examples include a spinning top or the Earth rotating on its axis.

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Periodic Motion: Motion that repeats itself at regular intervals of time is called periodic motion. A simple pendulum or the motion of a swing are common examples.

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Speed is a scalar quantity representing the rate at which an object covers distance, while Velocity is a vector quantity representing speed in a specific direction.

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Uniform Motion occurs when an object covers equal distances in equal intervals of time. Non-uniform motion occurs when the speed of the object changes over time.

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Acceleration is the rate of change of velocity. If an object speeds up, slows down, or changes direction, it is accelerating.

📐Formulae

Speed(s)=Distance(d)Time(t)Speed (s) = \frac{Distance (d)}{Time (t)}

Average Speed=Total Distance TraveledTotal Time TakenAverage\ Speed = \frac{Total\ Distance\ Traveled}{Total\ Time\ Taken}

Velocity(v)=Displacement(Δx)Time(t)Velocity (v) = \frac{Displacement (\Delta x)}{Time (t)}

Acceleration(a)=v−utAcceleration (a) = \frac{v - u}{t}

💡Examples

Problem 1:

A car travels a distance of 150 km150\ km in 3 hours3\ hours. What is the average speed of the car in km/hkm/h and m/sm/s?

Solution:

Speed=150 km3 h=50 km/hSpeed = \frac{150\ km}{3\ h} = 50\ km/h To convert to m/sm/s: 50 ×1000 m3600 s=50 ×518≈13.89 m/s50\ \times \frac{1000\ m}{3600\ s} = 50\ \times \frac{5}{18} \approx 13.89\ m/s

Explanation:

Average speed is calculated by dividing the total distance by the total time. To convert km/hkm/h to m/sm/s, we multiply by 518\frac{5}{18}.

Problem 2:

A cyclist starts from rest and reaches a velocity of 12 m/s12\ m/s in 4 seconds4\ seconds. Calculate the acceleration.

Solution:

Given: initial velocity u=0 m/su = 0\ m/s, final velocity v=12 m/sv = 12\ m/s, and time t=4 st = 4\ s. a=v−uta = \frac{v - u}{t} a=12 m/s−0 m/s4 s=3 m/s2a = \frac{12\ m/s - 0\ m/s}{4\ s} = 3\ m/s^2

Explanation:

Acceleration is the change in velocity divided by the time taken for that change. Since the cyclist started from rest, the initial velocity is zero.

Problem 3:

A train travels at a constant speed of 60 km/h60\ km/h for 2 hours2\ hours and then at 80 km/h80\ km/h for the next 3 hours3\ hours. Calculate the total average speed.

Solution:

Distance 1: d1=60 km/h×2 h=120 kmd_1 = 60\ km/h \times 2\ h = 120\ km Distance 2: d2=80 km/h×3 h=240 kmd_2 = 80\ km/h \times 3\ h = 240\ km Total Distance: 120+240=360 km120 + 240 = 360\ km Total Time: 2+3=5 h2 + 3 = 5\ h Average Speed=360 km5 h=72 km/hAverage\ Speed = \frac{360\ km}{5\ h} = 72\ km/h

Explanation:

To find the average speed for a multi-part journey, calculate the total distance covered in all parts and divide it by the total time elapsed.