13.0.0 : CONCEPT OF SPEED:
Speed can be defined as the time rate of change of distance. Speed is a scalar quantity.
S.I. UNIT OF SPEED:
The s.I. unit of speed ois meter per second m/s or ms¹
FORMULA OF SPEED:
the formula of speed is ,
Speed = distance travelled by object / time taken to travel the distance
Speed = distance / time
APPLICATION OF FORMULA TO SOLVE PROBLEMS:
EXAMPLE 1:
A train travelled a distance of 250 metres in 3½ minutes. Calculate the speed of the train.
SOLUTION:
data given in the question:
distance = 250m,
time = 3½minutes = 3½ * 60 seconds = 7/2 * 60 seconds = 210 seconds
Formula : speed = distance / time
Substitution : speed = 250 / 210 = 1.19 m/s
Therefore, speed = 1.19 m/s
EXAMPLE 2:
Calculate the distance traveled by a train in 2½ minutes if the speed of the train is 2.25 m/s.
SOLUTION:
Data given in the question:
Speed = 2.25 m/s ,
time = 2½ minutes = 2½ * 60 seconds = 5/2 * 60 sec = 150 seconds
Formula : Speed = distance / time
Substitution : 2.25 = distance / 150 ➡ distance = 2.25 * 150 = 337.5 meters
Distance travelled = 337.5 meters
AVERAGE SPEED:
Average speed is the total time rate of change of total distance. The s.I. unit of average speed is also meter per second, m/s.
FORMULA OF AVERAGE SPEED:
Average speed = total distance travelled by object t / total time taken
APPLICATION OF FORMULA:
EXAMPLE 1:
CONCEPT OF VELOCITY:
Velocity is the time rate of change of displacement. Velocity is a vector quantity. It is measured in meter per second, m/s.
FORMULA OF VELOCITY:
Velocity = displacement / time ➡ velocity = distance / time
APPLICATION OF FORMULA:
EXAMPLE 1:
Calculate the velocity of a train whose displacement in 3minutes is 324meters.
SOLUTION:
data given in the question:
Displacement= 324 meters,
Time = 3 minutes = 3 * 60 Sec = 180 Sec
Formula: velocity = displacement / time.
Substitution:
velocity = 324 / 180 ➡ velocity = 1.8 m/s
EXAMPLE 2:
What is the velocity of a car if the car travelled a distance of 12.5 meters in 1½ minutes?
SOLUTION:
Data given in the question:
Distance = 12.5 m
Time = 1½ min = ¹½ * 60 Sec = 3/2 * 60 Sec = 90 Sec.
Formula: velocity = distance / time
Substitution: velocity = 12.5 / 90. ➡ velocity = 0.139 m/s
UNIFORM SPEED:
Uniform speed is the constant time rate of changs of distance no matter how small the time may be.
UNIFORM VELOCITY:
Uniform velocity is the constant time rate of changs of displacement no matter how small the time may be.
INSTANTANEOUS VELOCITY:
instantaneous velocity of an object is the velocity of the object at a particular instant.
Note:
Speed and velocity are the same because they have the same units.
Also, you must take note that that distance - time graph of speed is the same for velocity. Speed and velocity are two similar things. Distance - time graph is also called displacement - time graph which is commonly used for velocity.
DISTANCE - TIME GRAPH OF SPEED :
The distance - time graph of speed is obtained by plotting different values of distance on the vertical axis against different values of time on the horizontal axis. This is shown in the figure below:
Distance - time graph of non uniform speed. Distance - time graph of uniform speed
figure 1 
figure 2
Figure 1 is a distance - time graph for a speed that increases with time while figure 2 is distance- time graph of speed that remains constant with time.
SLOPE OF DISTANCE - TIME GRAPH:
.
The slope of the graph represent the speed of the object that undergo the motion.
Slope = change in distance / change in time
Slope = d₂ - d₁ / t₂ - t₁ ➡ slope = distance / time ➡. Slope = speed.
From figure 2 above, the slope of the graph is zero. This is so because the change in the distance of the object is zero. That is d₂ - d₁ = 0. It means that the speed of the object remain constant with time.
Therefore,
d₂ = d₁
Slope = d₂ - d₁ / t₂ - t₁ ➡. Slope = 0 / t₂ - t₁ = 0 / t . ➡ slope = 0 / t = 0
Therefore,
speed = zero .
EXERCISES:
Speed can be defined as the time rate of change of distance. Speed is a scalar quantity.
S.I. UNIT OF SPEED:
The s.I. unit of speed ois meter per second m/s or ms¹
FORMULA OF SPEED:
the formula of speed is ,
Speed = distance travelled by object / time taken to travel the distance
Speed = distance / time
APPLICATION OF FORMULA TO SOLVE PROBLEMS:
EXAMPLE 1:
A train travelled a distance of 250 metres in 3½ minutes. Calculate the speed of the train.
SOLUTION:
data given in the question:
distance = 250m,
time = 3½minutes = 3½ * 60 seconds = 7/2 * 60 seconds = 210 seconds
Formula : speed = distance / time
Substitution : speed = 250 / 210 = 1.19 m/s
Therefore, speed = 1.19 m/s
EXAMPLE 2:
Calculate the distance traveled by a train in 2½ minutes if the speed of the train is 2.25 m/s.
SOLUTION:
Data given in the question:
Speed = 2.25 m/s ,
time = 2½ minutes = 2½ * 60 seconds = 5/2 * 60 sec = 150 seconds
Formula : Speed = distance / time
Substitution : 2.25 = distance / 150 ➡ distance = 2.25 * 150 = 337.5 meters
Distance travelled = 337.5 meters
AVERAGE SPEED:
Average speed is the total time rate of change of total distance. The s.I. unit of average speed is also meter per second, m/s.
FORMULA OF AVERAGE SPEED:
Average speed = total distance travelled by object t / total time taken
APPLICATION OF FORMULA:
EXAMPLE 1:
CONCEPT OF VELOCITY:
Velocity is the time rate of change of displacement. Velocity is a vector quantity. It is measured in meter per second, m/s.
FORMULA OF VELOCITY:
Velocity = displacement / time ➡ velocity = distance / time
APPLICATION OF FORMULA:
EXAMPLE 1:
Calculate the velocity of a train whose displacement in 3minutes is 324meters.
SOLUTION:
data given in the question:
Displacement= 324 meters,
Time = 3 minutes = 3 * 60 Sec = 180 Sec
Formula: velocity = displacement / time.
Substitution:
velocity = 324 / 180 ➡ velocity = 1.8 m/s
EXAMPLE 2:
What is the velocity of a car if the car travelled a distance of 12.5 meters in 1½ minutes?
SOLUTION:
Data given in the question:
Distance = 12.5 m
Time = 1½ min = ¹½ * 60 Sec = 3/2 * 60 Sec = 90 Sec.
Formula: velocity = distance / time
Substitution: velocity = 12.5 / 90. ➡ velocity = 0.139 m/s
UNIFORM SPEED:
Uniform speed is the constant time rate of changs of distance no matter how small the time may be.
UNIFORM VELOCITY:
Uniform velocity is the constant time rate of changs of displacement no matter how small the time may be.
INSTANTANEOUS VELOCITY:
instantaneous velocity of an object is the velocity of the object at a particular instant.
Note:
Speed and velocity are the same because they have the same units.
Also, you must take note that that distance - time graph of speed is the same for velocity. Speed and velocity are two similar things. Distance - time graph is also called displacement - time graph which is commonly used for velocity.
DISTANCE - TIME GRAPH OF SPEED :
The distance - time graph of speed is obtained by plotting different values of distance on the vertical axis against different values of time on the horizontal axis. This is shown in the figure below:
Distance - time graph of non uniform speed. Distance - time graph of uniform speed
figure 1 
figure 2Figure 1 is a distance - time graph for a speed that increases with time while figure 2 is distance- time graph of speed that remains constant with time.
SLOPE OF DISTANCE - TIME GRAPH:
. The slope of the graph represent the speed of the object that undergo the motion.
Slope = change in distance / change in time
Slope = d₂ - d₁ / t₂ - t₁ ➡ slope = distance / time ➡. Slope = speed.
From figure 2 above, the slope of the graph is zero. This is so because the change in the distance of the object is zero. That is d₂ - d₁ = 0. It means that the speed of the object remain constant with time.
Therefore,
d₂ = d₁
Slope = d₂ - d₁ / t₂ - t₁ ➡. Slope = 0 / t₂ - t₁ = 0 / t . ➡ slope = 0 / t = 0
Therefore,
speed = zero .
EXERCISES:
i love it
ReplyDelete