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

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.

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.