Question

1. a cars velocity increases from 5.0 m/s to 25.0 m/s in a time interval of 5.0 s. what is its average acceleration?
2. a bus is moving at 30.0 m/s. the driver steps on the brakes, and the bus stops in 6.0 s. what is the average acceleration of the bus while braking?
3. a cars velocity increases from 2.0 m/s at 1.0 s to 16 m/s at 4.5 s. what is the cars average acceleration?
4. a car goes faster and faster backwards on a long drive way. its velocity changes from -2.0 m/s to -9.0 m/s in a 2.0 s time interval. find its acceleration
5. a race car slows down from 36 m/s to 15 m/s over 3 s time interval. what is its acceleration?

Explanation:

Step1: 確認加速度公式

加速度公式為$a=\frac{v - u}{t}$，其中$v$是末速度，$u$是初速度，$t$是時間間隔。

Step2: 計算第一題

已知$u = 5.0\ m/s$，$v = 25.0\ m/s$，$t = 5.0\ s$，代入公式$a=\frac{v - u}{t}=\frac{25.0 - 5.0}{5.0}=\frac{20.0}{5.0}=4.0\ m/s^{2}$。

Step3: 計算第二題

已知$u = 30.0\ m/s$，$v = 0\ m/s$（停止），$t = 6.0\ s$，代入公式$a=\frac{v - u}{t}=\frac{0 - 30.0}{6.0}=- 5.0\ m/s^{2}$。

Step4: 計算第三題

$u = 2.0\ m/s$，$v = 16\ m/s$，$t=4.5 - 1.0 = 3.5\ s$，代入公式$a=\frac{v - u}{t}=\frac{16 - 2.0}{3.5}=\frac{14}{3.5}=4.0\ m/s^{2}$。

Step5: 計算第四題

$u=-2.0\ m/s$，$v = - 9.0\ m/s$，$t = 2.0\ s$，代入公式$a=\frac{v - u}{t}=\frac{-9.0-(-2.0)}{2.0}=\frac{-9.0 + 2.0}{2.0}=\frac{-7.0}{2.0}=-3.5\ m/s^{2}$。

Step6: 計算第五題

$u = 36\ m/s$，$v = 15\ m/s$，$t = 3\ s$，代入公式$a=\frac{v - u}{t}=\frac{15 - 36}{3}=\frac{-21}{3}=-7.0\ m/s^{2}$。

Answer:

1. $4.0\ m/s^{2}$
2. $-5.0\ m/s^{2}$
3. $4.0\ m/s^{2}$
4. $-3.5\ m/s^{2}$
5. $-7.0\ m/s^{2}$