# StudySquare

This page covers the following topics:

1. Velocity

2. Rotational motion

3. Terminal velocity

4. Velocity-time graphs for terminal velocity

The velocity of an object is its speed in a particular direction. While speed is a scalar only measured by its magnitude, velocity is a vector quantity, since it is described both by its magnitude and direction. Velocity is calculated using the same equation as speed; however, velocity usually refers to a specific time and has a direction.

Velocity is usually measured in m/s or km/h, although other compound units may be used. To convert the value of a velocity from m/s to km/h, multiply the value by 3.6. To convert velocity from km/h to m/s, divide by 3.6.

An object moving in a circular path at a constant speed is constantly changing direction, meaning that the velocity of the object is changing. Since the velocity of the object is not constant, the object must be accelerating, and thus there must be a resultant force acting on it to cause this acceleration. This force is called centripetal force and it acts towards the centre of the circle at 90ยฐ angle to the velocity. This acceleration does not affect the speed, only the direction of the velocity. The centripetal force is the resultant of all forces acting in the direction towards the centre of the circle it is travelling through.

Any object dropped near the surface of the Earth will accelerate downwards due to the force of gravity. As the speed of the object increases, the frictional forces (drag/air resistance) increase too. When the frictional forces increase enough to match the weight of the object, the resultant force on the object will be 0. Since there is no resultant force, the object will no longer be accelerating and will be travelling at a constant velocity called the terminal velocity.

In the case of a skydiver, when the parachute is opened, the air resistance suddenly increases due to the great surface area of the parachute, causing the skydiver to slow down. As the speed of the skydiver decreases, the air resistance force decreases too, until a new terminal velocity is reached when the weight of the skydiver and the air resistance become equal again.

The motion of a falling object that reaches terminal velocity can be modelled by the given velocity-time graph. The beginning of the graph shows the acceleration of the object downwards due to its weight. The slope then starts to decrease as the resistive forces start to increase with increasing speed. Eventually, the graph flattens out as the object reaches its constant terminal velocity.

# 1

Anna cycles via a straight road to a park which is 2 km west from her house and then cycles via the same road back. On her way home she stops at a bakery which is 800 m from home. Given that her journey from park to bakery takes her 3 minutes, find her velocity to 3 significant figures towards the end of her journey. Assume that Anna cycles at a constant speed.

Her displacement from her house at the end of the journey is 2 ร 1000 m โ 800 m = 1200 m.

Converting time to seconds, 3 minutes = 3 ร 60 seconds = 180 s.

Using v = d รท t, velocity = 1200 รท 180 = 6.67 m/s (to 3 significant figures).

Towards the end of her journey Anna is travelling in opposite direction, that is, east.

6.67 m/s east

# 2

Use Newton's second law to explain terminal velocity.

An object is said to reach terminal velocity when its weight and the air resistance acting on it are equal. This results in there being no resultant force acting on the object. According to Newton's second law, the object will have no acceleration and thus will be falling at a consant velocity called the terminal velocity.

no resultant force โ no acceleration โ constant (terminal) velocity

# 3

Explain how an object travelling at a constant speed in a circle is also accelerating.

Since the object is moving in a circle, it is constantly changing direction, therefore the velocity is also changing. For the velocity to be changing, the object must be accelerating, therefore an object moving in a circle at a constant speed is also accelerating.

change in direction โ change in velocity โ acceleration

# 4

A runner is running up and down a straight track of 80 m. She runs the full track north once, turns back and runs to the half-point of the track. Given that this takes her 12 seconds, calculate the runner's velocity at the beginning of the exercise. Assume that the runner has a constant speed.

total distance traveled by the runner = 80 m + 80 m ร 0.5 = 120 m

Using v = d/t, average speed = 120 m/12 s = 10 m/s.

Since at the beginning the runner is travelling north the initial velocity will also be in the same direction.

10 m/s north

# 5

State and explain the force that acts as the centripetal force that allows the Moon to orbit the Earth.

Modelling the Earth as the centre of the circle the Moon is orbitting in, the centripetal force is the gravitational pull of the Earth on the Moon, which acts in the direction towards the Earth at the centre of the orbit.

gravitational pull acting towards the Earth

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