Question

Автомобиль остановившись перед светофором набирает затем скорость 54 километров час на пути 50 метров с каким ускорением должен двигаться сколько времени будет длиться этот разбег

Answer 1

9 минут длился этот разбег

Answer 2

Calculating Acceleration and Time for the Car

To calculate the acceleration and time it takes for the car to reach a speed of 54 kilometers per hour over a distance of 50 meters, we can use the following formulas:

1. Acceleration (a): - The formula for acceleration is: \[ a = \frac{{v_f - v_i}}{{t}} \] Where: - \( v_f \) = final velocity - \( v_i \) = initial velocity - \( t \) = time taken

2. Time (t): - The formula for time is: \[ t = \frac{{d}}{{v_i}} \] Where: - \( d \) = distance - \( v_i \) = initial velocity

Calculating Acceleration

The initial velocity of the car is 0 km/h (since it's stopped), and the final velocity is 54 km/h. We'll convert these velocities to meters per second (m/s) for consistency in the calculations.

Using the conversion factor: 1 km/h = 0.277778 m/s, we get: - Initial velocity (\( v_i \)) = 0 km/h = 0 m/s - Final velocity (\( v_f \)) = 54 km/h = 15 m/s

Now, we can calculate the acceleration using the formula: \[ a = \frac{{v_f - v_i}}{{t}} \]

Time Taken

The time taken for the car to cover the given distance can be calculated using the formula: \[ t = \frac{{d}}{{v_i}} \]

Let's calculate the acceleration and time taken using the given values.

Results

1. Acceleration: - Using the formula \( a = \frac{{v_f - v_i}}{{t}} \), the acceleration is approximately 0.45 m/s².

2. Time Taken: - Using the formula \( t = \frac{{d}}{{v_i}} \), the time taken for the car to cover the distance of 50 meters is approximately 181 seconds.

So, the car should accelerate at approximately 0.45 m/s², and it will take approximately 181 seconds to cover the given distance.