QuestionA roller coaster accelerates from rest to $55 \mathrm{~m/s}$ in 4 seconds. Find the acceleration rate. Given: $v_f = 55 \mathrm{~m/s}$ , $t = 4$ s, $v_i = 0 \mathrm{~m/s}$ . Solve for $a$ .

Studdy Solution

STEP 1

Assumptions1. The initial velocity of the roller coaster is0 m/s (it starts from rest) . The final velocity of the roller coaster is55 m/s3. The time taken for this change in velocity is4 seconds4. The acceleration is constant during this time

STEP 2

We will use the formula for acceleration, which is defined as the change in velocity divided by the change in time.
$Acceleration = \frac{Final\, Velocity - Initial\, Velocity}{Time}$

STEP 3

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

STEP 4

implify the numerator in the fraction.
$Acceleration = \frac{55\, m/s}{4\, s}$

STEP 5

Calculate the acceleration.
$Acceleration = \frac{55\, m/s}{4\, s} =13.75\, m/s^2$ The acceleration rate of the roller coaster is $13.75 \, m/s^2$ .

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QuestionA roller coaster accelerates from rest to $55 \mathrm{~m/s}$ in 4 seconds. Find the acceleration rate. Given: $v_f = 55 \mathrm{~m/s}$ , $t = 4$ s, $v_i = 0 \mathrm{~m/s}$ . Solve for $a$ .

Studdy Solution

STEP 1

Assumptions1. The initial velocity of the roller coaster is0 m/s (it starts from rest) . The final velocity of the roller coaster is55 m/s3. The time taken for this change in velocity is4 seconds4. The acceleration is constant during this time

STEP 2

We will use the formula for acceleration, which is defined as the change in velocity divided by the change in time.
$Acceleration = \frac{Final\, Velocity - Initial\, Velocity}{Time}$

STEP 3

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

STEP 4

implify the numerator in the fraction.
$Acceleration = \frac{55\, m/s}{4\, s}$

STEP 5

Calculate the acceleration.
$Acceleration = \frac{55\, m/s}{4\, s} =13.75\, m/s^2$ The acceleration rate of the roller coaster is $13.75 \, m/s^2$ .

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QuestionA roller coaster accelerates from rest to 55 m/s55 \mathrm{~m/s}55 m/s in 4 seconds. Find the acceleration rate. Given: vf=55 m/sv_f = 55 \mathrm{~m/s}vf​=55 m/s, t=4t = 4t=4 s, vi=0 m/sv_i = 0 \mathrm{~m/s}vi​=0 m/s. Solve for aaa.

Studdy Solution

STEP 1

Assumptions1. The initial velocity of the roller coaster is0 m/s (it starts from rest) . The final velocity of the roller coaster is55 m/s3. The time taken for this change in velocity is4 seconds4. The acceleration is constant during this time

STEP 2

We will use the formula for acceleration, which is defined as the change in velocity divided by the change in time.Acceleration=Final Velocity−Initial VelocityTimeAcceleration = \frac{Final\, Velocity - Initial\, Velocity}{Time}Acceleration=TimeFinalVelocity−InitialVelocity​

STEP 3

Now, plug in the given values for the initial velocity, final velocity, and time into the formula.Acceleration=55 m/s−0 m/s sAcceleration = \frac{55\, m/s -0\, m/s}{\, s}Acceleration=s55m/s−0m/s​

STEP 4

implify the numerator in the fraction.Acceleration=55 m/s4 sAcceleration = \frac{55\, m/s}{4\, s}Acceleration=4s55m/s​

STEP 5

Calculate the acceleration.Acceleration=55 m/s4 s=13.75 m/s2Acceleration = \frac{55\, m/s}{4\, s} =13.75\, m/s^2Acceleration=4s55m/s​=13.75m/s2The acceleration rate of the roller coaster is 13.75 m/s213.75 \, m/s^213.75m/s2.

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QuestionA roller coaster accelerates from rest to $55 \mathrm{~m/s}$ in 4 seconds. Find the acceleration rate. Given: $v_f = 55 \mathrm{~m/s}$ , $t = 4$ s, $v_i = 0 \mathrm{~m/s}$ . Solve for $a$ .

We will use the formula for acceleration, which is defined as the change in velocity divided by the change in time.
$Acceleration = \frac{Final\, Velocity - Initial\, Velocity}{Time}$

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

implify the numerator in the fraction.
$Acceleration = \frac{55\, m/s}{4\, s}$

Calculate the acceleration.
$Acceleration = \frac{55\, m/s}{4\, s} =13.75\, m/s^2$ The acceleration rate of the roller coaster is $13.75 \, m/s^2$ .