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Motion - Rest and Motion

Grade 7ICSE

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

🔑Concepts

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An object is said to be at Rest if it does not change its position with respect to its immediate surroundings and a reference point.

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An object is said to be in Motion if it changes its position with respect to its surroundings and a reference point over time.

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Rest and Motion are Relative: An object can be at rest with respect to one observer but in motion with respect to another. For example, a person sitting in a moving train is at rest relative to the seat but in motion relative to the trees outside.

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Translatory Motion: When all parts of an object move the same distance in the same interval of time. It is divided into Rectilinear (straight line) and Curvilinear (curved path) motion.

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Rotatory Motion: When an object spins around a fixed axis passing through it, such as a spinning top or a ceiling fan.

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Oscillatory Motion: The 'to and fro' movement of an object about its mean position, like a simple pendulum.

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Periodic Motion: Motion that repeats itself after equal intervals of time, such as the revolution of the Earth around the Sun (T≈365.25T \approx 365.25 days).

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Speed: It is defined as the distance traveled by an object per unit of time. It is a scalar quantity. The S.I. unit of speed is m/sm/s or ms−1m s^{-1}.

📐Formulae

v=stv = \frac{s}{t}

Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}

1 km/h=518 m/s1 \text{ km/h} = \frac{5}{18} \text{ m/s}

1 m/s=185 km/h1 \text{ m/s} = \frac{18}{5} \text{ km/h}

💡Examples

Problem 1:

A car covers a distance of 360 km360 \text{ km} in 5 hours5 \text{ hours}. Find its speed in km/hkm/h and m/sm/s.

Solution:

Speed v=360 km5 h=72 km/hv = \frac{360 \text{ km}}{5 \text{ h}} = 72 \text{ km/h}. To convert to m/sm/s: 72×518 m/s=4×5=20 m/s72 \times \frac{5}{18} \text{ m/s} = 4 \times 5 = 20 \text{ m/s}.

Explanation:

We first use the formula v=stv = \frac{s}{t} to find the speed in the given units. Then, we apply the conversion factor 518\frac{5}{18} to obtain the value in S.I. units.

Problem 2:

An athlete runs a circular track of length 400 m400 \text{ m} in 50 seconds50 \text{ seconds}. Calculate the speed.

Solution:

v=400 m50 s=8 m/sv = \frac{400 \text{ m}}{50 \text{ s}} = 8 \text{ m/s}.

Explanation:

Speed is calculated by dividing the total path length (distance) by the time taken, regardless of the shape of the path.

Problem 3:

A train travels at a speed of 90 km/h90 \text{ km/h} for 20 minutes20 \text{ minutes}. How much distance does it cover?

Solution:

v=90 km/hv = 90 \text{ km/h}, t=20 min=2060 h=13 ht = 20 \text{ min} = \frac{20}{60} \text{ h} = \frac{1}{3} \text{ h}. Distance s=v×t=90×13=30 kms = v \times t = 90 \times \frac{1}{3} = 30 \text{ km}.

Explanation:

Distance is the product of speed and time. It is crucial to ensure that time units (hh) match the speed units (km/hkm/h) before multiplication.