Graphing Motion 运动图像 英文课件

(b) What is the displacement of the car during the first 10 s of its motion?
• Displacement = final position – initial position • = +5m – 0m = +5m • i.e. 5m north
• Velocity – Read directly from the graph • Acceleration – Calculate the gradient of the graph • Displacement – Calculate the area under the graph.
Velocity: e.g. What is the velocity at t = 3 s?
i.e. 0.25ms-1 south
(f) Calculate the average speed of the car during its 20s trip
total distance traveled average speed = time taken
Distance traveled = 10m + 10m + 5m = 25m
What if the graph isn’t a straight line?
∆y velocity = ∆x
∆y ∆x
Exercise (an example)
(a) Describe the motion of the car
(a)
Starting position
• During the first 4 s, the car travels 10m north at a constant velocity. • For the next 2 s then car is a rest. • The car then reverses direction, traveling south at a constant velocity between 6 and 14 s. • At t = 14 seconds, the car passes through its start point. • The car then decelerates, coming to rest 5m south of this point after a further 6 s.
12.5m
- 12.5m gradient ≈ = − 0.70ms −1 18s
18m
So, instantaneous velocity = 0.70ms-1 south
8.3 Questions Pages 226-227
Answer questions1-7
Describing the Motion…
(b) Calculate the cyclist’s displacement after the first 5 s.
Velocity (ms-1)
3 2 1 0 -1 -2 1 2 3 4 5 6 7 8 9 10
Note: • Positive area = positive displacement • Negative Area = negative displacement
= positive area = negative area
Velocity (ms-1)
3 2 1 0 -1 -2 1 2 3 4 5
Key words
• • • • • • • • Speed up 加速 Slow down （unifromly）(匀)减速 ） 匀 减速 Stationary 静止 At a constant rate 匀速 Gradient 斜率、坡度 斜率、 Position-time graph Velocity against time graph Acceleration-time graph
(i.e. it is getting slower)
Slope is getting less steep
Exercise: Plot a Position-time graph for the three cars.
• Which of the cars are accelerating? • Which car has the largest acceleration?
(f) Calculate the average speed of the car during its 20m trip
25m -1 so, average speed = = 1.25 ms 20s
(g) Calculate the instantaneous velocity of the car at t = 18 s.
(a) Describe the motion of the car
Velocity (ms-1)
3 2 1 0 -1 -2 1 2 3 4 5 6 7 8 9 10
Time (s)
•From the 7s to threes, the cyclist cyclist moves ••Between first t = 8 he remains stationary. in For t = 5s and 6s, seconds the continues the same direction with ofconstant velocity of at a constant velocity a +3ms-1. •He -1. -2msthen accelerates in the opposite direction •for 1 s, reaching a decelerates-2ms-1. The cyclist then velocity of at a constant •He then decelerates constantly for 2 s, t = 5s rate for the next 2 s, coming to rest at coming to rest at t = 10s.
s average velocity = = gradient ∆t + 10m −1 = = +2.5ms i.e. 2.5ms-1 north 4s
(e) Calculate the average velocity of the car during its 20s trip
s - 5m −1 average velocity = = = −0.25ms ∆t 20 s
Velocity (ms-1)
6 5 4 3 2 1 0 0 1 2 3 4
Displacement During the first 3 seconds = area Under graph
Displacement = Area of Triangle Time (s) = ½ x 3s x 5ms-1 = +7.5m
Velocity (ms-1)
6 5 4 3 2 1 0 0 1 2 3 4
At t = 3 s Velocity = +5ms-1
Time (s)
Acceleration: e.g. what is the acceleration
at t = 3 s?
Velocity (ms-1)
6 5 4 3 2 1 0 0
First, we need to draw a tangeate the gradient of the tangent
(g) Calculate the instantaneous velocity of the car at t = 18 s.
(c) What distance does the car travel during the first 10 seconds?
• Distance traveled during first 10 seconds = 10m + 5m = 15m
(d) Calculate the average velocity of the car during the first 4 s.
Position/time graphs
The position-time graph for an object moving at a constant velocity is shown below:
We calculate the velocity from the gradient of the graph
Describe the motion of this object…
The car is accelerating.
(i.e. it is getting faster)
Slope is Getting steeper
..what about this object?
The car is decelerating.
∆t
Acceleration = gradient ∆v
∆ v 5ms a= = ∆t 3s
4
−1
= +1.67 ms-2
1 2 3
Time (s)
Displacement: What is the displacement of
the car during the first 3 s of motion?
Object moving with a constant velocity Object accelerating
Positive direction Positive direction
(constant a )
Object decelerating
Velocity