Question

A car acclerates uniformly from to a rest to a speed 23.7 km/h in 6.5 s.Find the car travels during the time.(Displacement with constant uniform accleration).My only problem is the conversion

Answer 1

[AI-generated answer — Step-by-Step Bot]

To determine the displacement of the car during the given time, we need to convert the speed from km/h to m/s, as the unit of acceleration also needs to be in m/s².

1 km/h is equivalent to 1000 m / 3600 s = 5/18 m/s.

The final speed of the car is 23.7 km/h, which is equal to (23.7 * 5/18) m/s = 6.583 m/s (rounded to three decimal places).

The initial speed of the car is 0 m/s since it started from rest.

The time taken is 6.5 s.

To find the displacement, we can use the equation:

s = ut + (1/2)at^2

where:
s = displacement
u = initial velocity
t = time
a = acceleration

Since the acceleration is uniform, we can assume a = (v - u) / t, where v is the final velocity.

Thus, a = (6.583 m/s - 0 m/s) / 6.5 s = 1.012 m/s² (rounded to three decimal places).

Plugging the values into the equation:

s = 0 * 6.5 + (1/2) * 1.012 * (6.5)^2
s = 0 + 0.5 * 1.012 * 42.25
s = 21.38325 m (rounded to five decimal places)

Therefore, the car travels approximately 21.38325 meters during the given time of 6.5 seconds.

Answer 2

[AI-generated answer — Explain Bot]

To find the displacement of the car during the given time, we need to convert the given speed and time into a consistent unit system. Let's convert the given speed from km/h to m/s first.

1 km/h = 1000 m / 3600 s (conversion factor)

So, to convert 23.7 km/h to m/s:

23.7 km/h * (1000 m / 3600 s) = 6.583 m/s (rounded to three decimal places)

Now that we have the speed in m/s, we can use the following equation to find the displacement:

displacement = (initial velocity * time) + (0.5 * acceleration * time^2)

Given that the car starts from rest (initial velocity = 0), and assuming a constant uniform acceleration, we also need to find the acceleration. We can use the formula:

acceleration = change in velocity / time

Change in velocity = final velocity - initial velocity

In this case, final velocity = 6.583 m/s (as calculated above), and initial velocity = 0 m/s (rest).

acceleration = (6.583 m/s - 0 m/s) / 6.5 s

Now, let's calculate the acceleration:

acceleration = 1.012 m/s^2 (rounded to three decimal places)

Finally, substitute the values into the displacement equation:

displacement = (0 * 6.5) + (0.5 * 1.012 * 6.5^2)

displacement = 21.008 m (rounded to three decimal places)

Therefore, the car travels approximately 21.008 meters during the given time of 6.5 seconds.