1 Answer

Etella · Answer 1 · 2023-07-21T15:25:57+0000

First, find the acceleration using Newton's Second Law.

$\begin{gathered} F=ma \\ a=(F)/(m) \end{gathered}$

Where F = 8.10x10^5 N and m = 1.40x10^7 kg.

$a=\frac{8.10*10^5N}{1.40*10^7\operatorname{kg}}=5.79*10^(-2)\cdot(m)/(s^2)$

Then, use a formula that relates acceleration, initial velocity, final velocity, and time.

Solve for t because the problem is asking to find the time.

$\begin{gathered} v_f-v_0=at_{} \\ t=(v_f-v_0)/(a) \end{gathered}$

Where vf = 64 km/h, v0 = 0, and a = 5.79x10^-2 m/s^2. Before we continue, we need to transform the final velocity to m/s.

$v_f=64\cdot(km)/(h)\cdot\frac{1000m}{1\operatorname{km}}\cdot(1h)/(3600\sec)=17.78\cdot(m)/(s)$

Once we have the velocity transformed, we are able to find t.

$\begin{gathered} t=(17.78\cdot(m)/(s)-0)/(5.79*10^(-2)\cdot(m)/(s^2)) \\ t=3.07*10^2\sec \\ t=307\sec \end{gathered}$

But, the answer must be in minutes.

$t=307\sec \cdot(1\min)/(60\sec)=5.12\min$

Therefore, it takes 5.12 minutes.

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