A truck increases its speed from 8 m/s to 28 m/s over a distance of 120 m? How long does this take? Assume that the acceleration is constant
Why did the truck decide to speed up? Because it heard there was a "drive-thru" opportunity up ahead! Now, let's calculate how long this speedy adventure takes.
We can use the formula:
acceleration (a) = Δv / Δt
Where Δv is the change in velocity and Δt is the change in time.
Given that the initial velocity (u) is 8 m/s, the final velocity (v) is 28 m/s, and the distance (s) is 120 m.
First, let's calculate the acceleration:
a = (v - u) / t
Since the acceleration is constant, we can solve for time, t:
t = (v - u) / a
Plugging in the values:
t = (28 m/s - 8 m/s) / a
However, we don't know the value of acceleration yet. So, I'm afraid I can't give you a specific answer without that information. But remember, even if the truck is fast, it's always better to drive safely and avoid any unfortunate clown car pile-ups!
To calculate the time it takes for the truck to increase its speed, we can use the formula for time:
time = (final velocity - initial velocity) / acceleration
Given:
Initial velocity (u) = 8 m/s
Final velocity (v) = 28 m/s
Distance (s) = 120 m
Since the acceleration is assumed to be constant, we need to find the acceleration first. We can use the formula:
v^2 = u^2 + 2as
Rearranging the formula to solve for acceleration (a):
a = (v^2 - u^2) / 2s
Let's calculate the acceleration first:
a = (28^2 - 8^2) / (2 * 120)
a = (784 - 64) / 240
a = 720 / 240
a = 3 m/s^2
Now that we have the acceleration, we can calculate the time:
time = (28 - 8) / 3
time = 20 / 3
time ≈ 6.67 seconds
So, it takes approximately 6.67 seconds for the truck to increase its speed from 8 m/s to 28 m/s over a distance of 120 m, assuming a constant acceleration.
To find the time it takes for the truck to reach the final speed, we can use the equation:
v = u + at
Where:
v is the final speed (28 m/s),
u is the initial speed (8 m/s),
a is the acceleration,
t is the time taken.
We can rearrange the equation to solve for time (t):
t = (v - u) / a
In this case, the acceleration is constant. However, we need to find the value of acceleration. We can use the following equation to determine the acceleration:
v² = u² + 2as
Where:
v is the final speed (28 m/s),
u is the initial speed (8 m/s),
a is the acceleration,
s is the distance (120 m).
Rearranging the equation, we get:
a = (v² - u²) / (2s)
Plugging in the given values:
a = (28² - 8²) / (2 * 120)
a = (784 - 64) / 240
a = 720 / 240
a = 3 m/s²
Now we can substitute the values of a, v, and u into the equation for time (t):
t = (28 - 8) / 3
t = 20 / 3
t ≈ 6.67 seconds
Therefore, it takes approximately 6.67 seconds for the truck to increase its speed from 8 m/s to 28 m/s over a distance of 120 m with constant acceleration.
average velocity= 18m/s
time= distance/avg veloicity