Question

За какое время автомобиль, двигаясь из состояния покоя с ускорением0.6м/с ^2, пройдет 30м?

Answer 1

s=30    a=0.6    t=?

s=a*t²/2       t=√(2*s/a)=√(2*30/0.6)=10 c

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Answer 2

Calculating the Time Taken to Travel a Distance with Constant Acceleration

To calculate the time it takes for a car to travel a certain distance with a constant acceleration, we can use the following kinematic equation:

\[d = v_i t + \frac{1}{2} a t^2\]

Where: - \(d\) = distance traveled - \(v_i\) = initial velocity - \(a\) = acceleration - \(t\) = time

In this case, the car is starting from rest, so the initial velocity (\(v_i\)) is 0.

Applying the Kinematic Equation

Using the provided acceleration (\(a = 0.6 \, \text{m/s}^2\)) and the distance (\(d = 30 \, \text{m}\)), we can rearrange the kinematic equation to solve for time (\(t\)):

\[d = \frac{1}{2} a t^2\]

Calculating the Time

Let's calculate the time it takes for the car to travel 30 meters with an acceleration of 0.6 m/s\(^2\):

\[30 = \frac{1}{2} \times 0.6 \times t^2\]

Solving for \(t\):

\[t^2 = \frac{30 \times 2}{0.6}\]

\[t^2 = 100\]

\[t = \sqrt{100}\]

\[t = 10\]

So, the car will take 10 seconds to travel 30 meters with an acceleration of 0.6 m/s\(^2\).

Conclusion

Based on the calculations, the car, moving from rest with an acceleration of 0.6 m/s\(^2\), will take 10 seconds to travel a distance of 30 meters.