A car accelerates from 0m/s to 51m/s with a displacement of 75 m. What is the car's acceleration

V^2 = Vo^2 + 2a*d

a = (V^2-V0^2)/2d
a = (51^2-0)/150 = 17.34 m/s^2.

Well, it seems like the car is really in a hurry to get somewhere! Let's calculate its acceleration using the good old equation: acceleration = (final velocity - initial velocity) / time. But wait, we don't know the time yet. Don't worry, we can find it using the displacement and the average velocity: time = displacement / average velocity.

Since the displacement is given as 75 m and the final velocity is given as 51 m/s, let's find the average velocity first. To find the average velocity, we can use the formula: average velocity = (final velocity + initial velocity) / 2. However, the initial velocity is not given, so let's assume it is 0 m/s.

Using the formula, we can calculate the average velocity as follows: average velocity = (51 m/s + 0 m/s) / 2 = 25.5 m/s.

Now that we have the average velocity, we can calculate the time: time = displacement / average velocity = 75 m / 25.5 m/s ≈ 2.94 seconds.

Finally, using the first equation for acceleration: acceleration = (final velocity - initial velocity) / time, we can fill in the given values: acceleration = (51 m/s - 0 m/s) / 2.94 s ≈ 17.35 m/s².

So, after all that math, the car's acceleration is approximately 17.35 m/s². Keep in mind, this is assuming a constant acceleration throughout the entire displacement.

To find the car's acceleration, we can use the equation:

acceleration = (change in velocity) / (change in time)

Given:
Initial velocity (u) = 0 m/s
Final velocity (v) = 51 m/s

We have initial velocity and final velocity, but we do not have the change in time. However, we have the displacement (x) of the car, which can help us find the change in time.

We can use the equation of motion:

displacement (x) = (initial velocity (u) + final velocity (v)) / 2 * time

Given:
Displacement (x) = 75 m

Rearranging the equation, we can solve for time:

time = (displacement (x) * 2) / (initial velocity (u) + final velocity (v))

Plugging in the given values:

time = (75 * 2) / (0 + 51)
time = 150 / 51
time ≈ 2.94 seconds

Now that we have found the change in time, we can calculate the acceleration:

acceleration = (final velocity (v) - initial velocity (u)) / (change in time)

Plugging in the given values:

acceleration = (51 - 0) / 2.94
acceleration ≈ 17.35 m/s²

Therefore, the car's acceleration is approximately 17.35 m/s².

To calculate the car's acceleration, we can use the following formula:

Acceleration (a) = Change in velocity (Δv) / Change in time (Δt)

Since we have the initial velocity (0 m/s) and final velocity (51 m/s), we can calculate the change in velocity by subtracting the initial velocity from the final velocity:

Δv = Final velocity - Initial velocity
= 51 m/s - 0 m/s
= 51 m/s

To find the time taken for this acceleration, we need to know more information. The question only provides the displacement (75 m). Without the time, it is not possible to calculate acceleration solely based on the displacement. If you have any additional information, such as the time taken or the equation relating displacement, time, and acceleration, please provide it so that we can help you further.