Question

1. if a car with velocity of 3.0 m/s at t = 0.0 s accelerates at a rate of 5.0 m/s² for 3.5 s, what is its velocity at time t = 3.5 s?
2. how long will it take you to go from 2.0 m/s to 10.0 m/s if you are accelerating at a rate of 3.5 m/s²?
3. what must your initial velocity be if you accelerate at 3.2 m/s² for t = 3.3 s and have a final velocity of 20.0 m/s at the end of that time?
4. a car is coasting backwards down a hill at 3.0 m/s. after 2.5 s, the car is moving uphill at 4.5 m/s. what is the car’s average acceleration?
5. a bus is moving at 25 m/s. the driver steps on the brakes, and the bus stops in 3.0 s. what is the average acceleration of the bus?

Explanation:

6.

Step1: 確認公式

使用公式$v = v_0+at$，其中$v$是末速度，$v_0$是初速度，$a$是加速度，$t$是時間。

Step2: 代入數值

已知$v_0 = 3.0\ m/s$，$a = 5.0\ m/s^2$，$t = 3.5\ s$，代入公式得$v=3.0 + 5.0\times3.5$。

Step3: 計算結果

$v=3.0+17.5=20.5\ m/s$。

Step1: 確認公式

由$v = v_0+at$變形得$t=\frac{v - v_0}{a}$。

Step2: 代入數值

已知$v = 10.0\ m/s$，$v_0 = 2.0\ m/s$，$a = 3.5\ m/s^2$，代入得$t=\frac{10.0 - 2.0}{3.5}$。

Step3: 計算結果

$t=\frac{8.0}{3.5}\approx2.29\ s$。

Step1: 確認公式

由$v = v_0+at$變形得$v_0=v - at$。

Step2: 代入數值

已知$v = 20.0\ m/s$，$a = 3.2\ m/s^2$，$t = 3.3\ s$，代入得$v_0=20.0-3.2\times3.3$。

Step3: 計算結果

$v_0=20.0 - 10.56 = 9.44\ m/s$。

Answer:

$20.5\ m/s$

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