谭先生骑摩托车去咖啡店吃早餐。
他从静止开始，以恒定加速度在 15 秒内加速到 20 m/s 的速度。
然后他以 20 m/s 的恒定速度行驶接下来的 20 秒，然后在接下来的 10 秒内减速至静止。

它不会直接告诉你答案，而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

1. Identify the key points on the speed-time graph from the description.

Mr Tan starts from rest, so the graph starts at $(0,0)$ .

He reaches $20\text{ m/s}$ after $15\text{ s}$ , giving the point $(15,20)$ .

He then travels at $20\text{ m/s}$ for the next $20\text{ s}$ , so the time is $15+20=35\text{ s}$ , giving $(35,20)$ .

He comes to rest in the next $10\text{ s}$ , so the final time is $35+10=45\text{ s}$ , giving $(45,0)$ .

2. Draw the speed-time graph using straight line segments.

Draw straight line segments:

答案

Sketch a speed-time graph made of straight line segments joining
$(0,0) \to (15,20) \to (35,20) \to (45,0).$

1. Calculate the acceleration from rest to $20\text{ m/s}$ in $15$ seconds.

Acceleration
$=\frac{\text{change in speed}}{\text{time taken}}=\frac{20-0}{15}=\frac{4}{3}\text{ m/s}^2.$

答案

$\dfrac{4}{3}\text{ m/s}^2$

1. Find the total distance travelled from the area under the speed-time graph.

Distance travelled
$= \frac{1}{2}(15)(20) + (20)(20) + \frac{1}{2}(10)(20)$
$=150+400+100=650\text{ m}$

2. Divide the total distance by the total time to calculate the average speed.

Total time $=15+20+10=45\text{ s}$

Average speed
$=\frac{\text{total distance}}{\text{total time}}$
$=\frac{650}{45}=14.444\ldots$

答案

$\dfrac{700}{45}=15.6\text{ m/s}$

AI 分析，可能出错

用 AI 批改，圈出写错的那一步，并自动将你的薄弱点存入错题本，形成你的错因库。