QuestionA roller coaster accelerates from rest to $55 \mathrm{~m} / \mathrm{s}$ in 4 seconds. Find the distance traveled.

Studdy Solution

STEP 1

Assumptions1. The roller coaster starts from rest, meaning its initial velocity is0 m/s. . The roller coaster accelerates to a final velocity of55 m/s.
3. The time it takes for this acceleration is4 seconds.
4. The acceleration is uniform, meaning it is constant over the4 seconds.
5. We are asked to find the distance travelled during this time.

STEP 2

First, we need to find the acceleration of the roller coaster. Acceleration is the change in velocity divided by the time it takes for this change to occur.
$Acceleration = \frac{Final\, velocity - Initial\, velocity}{Time}$

STEP 3

Now, plug in the given values for the final velocity, initial velocity, and time to calculate the acceleration.
$Acceleration = \frac{55\, m/s -0\, m/s}{\, s}$

STEP 4

Calculate the acceleration.
$Acceleration = \frac{55\, m/s}{4\, s} =13.75\, m/s^2$

STEP 5

Now that we have the acceleration, we can find the distance travelled by the roller coaster. The formula for distance travelled under constant acceleration from rest is given by $Distance = \frac{1}{2} \times Acceleration \times Time^2$

STEP 6

Plug in the values for acceleration and time into the formula to calculate the distance.
$Distance = \frac{1}{2} \times13.75\, m/s^2 \times (4\, s)^2$

STEP 7

Calculate the distance travelled by the roller coaster.
$Distance = \frac{1}{2} \times13.75\, m/s^2 \times16\, s^2 =110\, m$ The roller coaster travels110 meters during this time.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms