# LINEAR MOTION: SPEED AND VELOCITY

Speed is the rate at which things move. Velocity is speed with a direction.

CONTENT

THE CONCEPT OF DISTANCE, SPEED, VELOCITY AND UNIFORM SPEED/VELOCITY

CALCULATIONS ON SPEED, VELOCITY AND ACCELARATION

VELOCITY – TIME GRAPH

THE CONCEPT OF DISTANCE, SPEED, VELOCITY AND UNIFORM SPEED/VELOCITY

Distance: Distance is the total movement of an object without considering the direction. We can define the distance, i.e. how much ground the object covers, despite its starting or ending point. In physical or daily use, distance can refer to physical length or estimates based on other criteria. The distance from point a to point b is sometimes expressed as {AB] In most cases, “distance from A to B” can be interchanged with “distance from B to A”.

Speed: Speed refers to the scalar of “the speed at which an object moves”. “Speed can be thought of as the rate at which an object covers a distance. Fast-moving objects have a higher speed and cover a relatively large distance in a short time. In contrast, a slow moving object has a lower speed; it covers a relatively small distance in the same time. An object that has no movement at all has zero speed.

Velocity: Velocity refers to the vector amount of “the rate at which an object changes its position”. Imagine a person moving quickly-one step forward, one step back-always back to the original starting position. While this may lead to a frenzy of activity, it will lead to zero speed. Because people always return to their original position, movement will never lead to a change in position. Since speed is defined as the rate of change in position, this movement results in zero speed. If a person in motion wants to maximize their speed, then the person must make every effort to maximize the number of shifts they shift from their original position.

Uniform speed/Velocity: If the speed of the body does not change with time, it is called uniform movement. For objects moving at uniform speed, the net external force is always equal to zero. An example of uniform movement is that the body slides on a frictionless surface at a constant speed. When an object travels an equal distance within an equal time interval.

CALCULATIONS ON SPEED, VELOCITY AND ACCELARATION

Speed velocity and acceleration

1. Speed = distance => S = d/f

time

1. Velocity = displacement =>s/t

time

Acceleration = final vel – initial vel

time taken

a = v – u

t

Note: The difference between speed and velocity is known from their units. Example: A driver travelling at a speed of 11skm/hr received a text message on his mobile phone.

How far is he in kilometers, 20sec later from when he received the text.

Speed = 115km/hr time = 20 (consent to hour by driving by 3600 =>20/3600 hr) distance =?

S = distance, d = speed x time

time

115 x 20/3600 = 2300/3600 = 0.639km

VELOCITY – TIME GRAPH

1. A car runs at a constant speed of 15mls for 300s and then accelerates uniformly to a speed of 25mls over a period of 20sec. This speed is maintained for 300sec before the car is brought to rest with uniform      deceleration in 30sec. draw a velo-time graph to represents the journey  and find 15mls to 25mls.

i. The acceleration whole the velocity changes from 15mls to 25mls

ii. The total distance travelled in this time described.

iii. The average speed over the time described.

Note:- Constant speed of 15mls is represented by AB drawn parallel to the time bar, for 300sec its represented by 0BH etc. Note:- Looking at the diagram above, shape of diagram I is a square, II is a trapezium, III square, IV triangle.

1. The acceleration a is equal to the slope of BC

a =c > = 25 – 15=10 = ½ = 0.5mls2

B > = 320 – 30020

1. In v – t graph, total distance is equal to the area and it is OABCDE

Area: OABCDE = ABHO + BCGH + CDFG + DEF

Area: OABCDE = Distance covered during constant speed of 15mls for 360sec

Area: ABHO = Distance covered during acceleration or velocity change from 15mls to 25mls

Area CDFG: Distance covered during when speed (25mls) is maintained for    300sec

Area DEF: Distance covered during uniform deceleration in 30 seconds

Total distance = OABCDE => ABHO + BCGH + CDFG + DEF

= Square + trapezium + square + triangle

AB X BH + ½(BH + CG) HG + (CP + PF) + ½ (FE X DF)

300 X 15 + ½(15 + 25) 20 + 300 X 25 + ½(30 X 25)

= 12775m

• Average speed = total distance travelled = 12775 => 19.65mls

Total time take                   650

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