# F.3 Physics Questions

A driver of moving car suddenly saw a dog running across the road. He applied the brake 0.5s later and the car decelerated uniformly to rest.

(a) Find the initial speed of the car in km/h.

(b) Find the area under the graph and state its physical meaning

A car is moving at a velocity of 70km/h. The driver then sees a 50km/h speed limit sign at a distance of 30m ahead. In order not to exceed the speed limit, find the minimum deceleration of the car.

Rating

以下我用hr代表hour﹐這些純屬個人喜好

1

(a)

From the graph

initial speed

=20 m/s

=20 (m/s)(1km/1000m)(3600 s/1 hr)

=72 km/hr

1 這是最保險的做法﹐雖然會做得慢些

2 題目已經給了初速﹐不用計算

(b)

Thr area under the graph

=area of rectangle+ area of triangle

=20*0.5+20*(2.5-0.5)/2

=10+20

=30 m

Its physical meaning is:

The total traveling distance of the car from the driver saw a dog until the car stopped moving.

1 由s=∫v dt 可知v-t曲線圖中所包圍的面積是距離。

2 又v-t曲線圖中所包圍的面積不是位移。

3 在這裡題目沒有問減速度﹐所以不用計算。

2

We notice that if the car pass through the speed limit sign at 50km/h, then the deceleration of the car should be at the minimum value.

We use v^2-u^2=2as

Here u= 70km/h, v=50km/h, s=30m=30/1000 km=0.03 km

50^2-70^2=2a(0.03)

a=-40000 kmhr^-2 (minus sign means decelerate)

Since

-40000 kmhr^-2

=-40000 (km/hr^2)(1000 m/1 km)(1 hr^2/3600*3600 s^2)

=-3.0864 ms^-2

So the minimum deceleration of the car is -3.0864 ms^-2

理論上可以首先全部換成 m/s 再做﹐不過因為題目有2個原始數據都是km/hr 所以若果直接用km/hr (注意30m轉成km都是完整數字﹐沒有捨入誤差) 計算出來的答案會準確些。

• 阿一
Lv 7

第1條問題

a)

v = u + at

0 = u + 0.5a

u = -0.5a

i.e. if the acceleration is -2km/h2, initial speed is 1km/h

it is in negative side coz it is deceleration

b)

the area under the graph can be found by considering the area of a triangle, while the area of a triangle can be computed by the formula (base * height / 2)

the area under the velocity-time graph is the displacement of the car

第2條問題

v2 = u2 + 2as

502 = 702 + 2a(30/1000)

2500 = 4900 + 6a/100

-2400 = 6a/100

6a = -240000

a = -40000

i.e. the minimum deceleration is -40000km/h2

2007-04-06 16:19:45 補充：

the acceleration can be found by finding the slope of the graph

2007-04-06 17:15:19 補充：

to convert -40000km/h^{-2} to SI unit (ms^{-2})1km = 1000m1hour = 3600sso -40000 * 1000/ 3600 / 3600 = -3.086ms^{-2}

2007-04-06 17:17:15 補充：

a = slope = (0 - 20) / (2.5 - 0.5) = -20/2 = -10so u = -0.5 * - 10 = 5ms^{-1}area = 20*0.5 + (2.5 - 0.5)*20/2= 30m

1. I think Q1 has miss one figure.

so I can&#39;t solve it.

2.Based on v^2 - u^2 = 2as,

(v= final speed,u= initial speed, a= acceleration, s=displacement)

(50/3.6)^2 - (70/3.6)^2 = 2(30)

a= -3.09 m/s^2

Therefore the minimum deceleration of the car is 3.09m/s^2

2007-04-06 19:03:50 補充：

1a.有graph就唔同哂 :P As we can see in the graph,the initial speed is 20m/s,20m/s = 20 x 1km/1000m x 3600s/1hour= 20 x 3.6km/hour= 72 km/hour

2007-04-06 19:04:06 補充：

b.the area under the graph is (0.5 2.5)s x 20m/s /2 =3s x 20m/s /2=30mTherefore the physical meaning of the graph is &quot;the distance of stopping the car&quot;.

Source(s): my physical knowledge