Suppose that an accelerating car goes from 0 mph to 58.6 mph in five seconds. Its velocity is given in the following table, converted from miles per hour to feet per second, so that all time measurements are in seconds. (Note: 1 mph is 22/15 feet per sec = 12/15 ft/s.) Find the average acceleration of the car over each of the first two seconds.

Question

Suppose that an accelerating car goes from 0 mph to 58.6 mph in five seconds. Its velocity is given in the following table, converted from miles per hour to feet per second, so that all time measurements are in seconds. (Note: 1 mph is 22/15 feet per sec = 12/15 ft/s.) Find the average acceleration of the car over each of the first two seconds.

t 0 1 2 3 4 5
v(t) 0.00 29.32 50.82 66.45 78.18 86.00

Answer 1

Edit:

first second
a = change in V/change in t
= 29.32/1 ft/s^2

second second
a = (50.82-29.32) /1 ft/s^2

ft/s^2 are the units

Answer 2

Well, since we're talking about a car, let's put on our imaginary driving goggles and calculate the average acceleration.

To find the average acceleration over the first two seconds, we need to determine the change in velocity and divide it by the change in time.

The change in velocity from t=0 to t=2 is v(2) - v(0) = 50.82 - 0.00 = 50.82 ft/s.

The change in time is 2 seconds.

To find the average acceleration, we divide the change in velocity by the change in time:

Average Acceleration = (Change in Velocity) / (Change in Time) = 50.82 ft/s / 2 s = 25.41 ft/s^2.

So, the average acceleration of the car over the first two seconds is 25.41 ft/s^2.

Now, if you excuse me, I need to go inflate my imaginary driving tires.

Answer 3

To find the average acceleration of the car over each of the first two seconds, we need to calculate the change in velocity and divide it by the time interval.

First, let's calculate the change in velocity over the first two seconds.

Change in velocity (Δv) = v(2) - v(0)
= 50.82 - 0.00
= 50.82 ft/s

Next, calculate the time interval for the first two seconds.

Time interval (Δt) = 2 - 0
= 2 seconds

Now, we can calculate the average acceleration.

Average acceleration = Δv / Δt
= 50.82 ft/s / 2 seconds
= 25.41 ft/s^2

Therefore, the average acceleration of the car over the first two seconds is 25.41 ft/s^2.

Answer 4

To find the average acceleration of the car over a given time interval, we can use the formula:

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

In this case, we want to find the average acceleration over the first two seconds. So we need to calculate the change in velocity and the change in time.

Change in velocity:
To find the change in velocity, we subtract the initial velocity from the final velocity. In this case, the initial velocity at t=0 is 0.00 ft/s, and the final velocity at t=2 is 50.82 ft/s. So the change in velocity is:

change in velocity = final velocity - initial velocity
= 50.82 ft/s - 0.00 ft/s
= 50.82 ft/s

Change in time:
The change in time is simply the difference between the final time and the initial time. In this case, the initial time is 0 seconds, and the final time is 2 seconds. So the change in time is:

change in time = final time - initial time
= 2 seconds - 0 seconds
= 2 seconds

Now we can calculate the average acceleration:

average acceleration = (change in velocity) / (change in time)
= 50.82 ft/s / 2 seconds
= 25.41 ft/s^2

Therefore, the average acceleration of the car over the first two seconds is 25.41 ft/s^2.

Answer 5

first second

a = change in V/change in t
= 29.32/1

second second
a = (50.82-29.32) /1