QuestionA train accelerates from rest to $60 \mathrm{~m/s}$ in $40 \mathrm{~s}$ . Find its acceleration. A boat slows from $18 \mathrm{~m/s}$ to stop in $6 \mathrm{~s}$ . Find its acceleration.

Studdy Solution

STEP 1

Assumptions1. The initial speed of the train is0 m/s. The final speed of the train is60 m/s3. The time taken for the train to reach this speed is40 s4. The acceleration is constant

STEP 2

The formula for acceleration is given by the change in velocity divided by the time taken for this change. Mathematically, this is represented as $Acceleration = \frac{Final\, speed - Initial\, speed}{Time}$

STEP 3

Now, plug in the given values for the initial speed, final speed, and time into the formula to calculate the acceleration.
$Acceleration = \frac{60\, m/s -0\, m/s}{40\, s}$

STEP 4

Calculate the acceleration.
$Acceleration = \frac{60\, m/s}{40\, s} =1.\, m/s^2$ The acceleration of the train is $1.\, m/s^2$ .

STEP 5

Assumptions for the boat problem1. The initial speed of the boat is18 m/s2. The final speed of the boat is0 m/s (as it comes to a stop)
3. The time taken for the boat to stop is s4. The deceleration (negative acceleration) is constant

STEP 6

We use the same formula for acceleration, but this time the initial speed is greater than the final speed, so the acceleration will be negative (indicating a slowdown or deceleration).
$Acceleration = \frac{Final\, speed - Initial\, speed}{Time}$

STEP 7

Now, plug in the given values for the initial speed, final speed, and time into the formula to calculate the acceleration.
$Acceleration = \frac{0\, m/s -18\, m/s}{6\, s}$

STEP 8

Calculate the acceleration.
$Acceleration = \frac{-18\, m/s}{6\, s} = -3\, m/s^2$ The acceleration (or in this case, deceleration) of the boat is $-3\, m/s^2$ .

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QuestionA train accelerates from rest to $60 \mathrm{~m/s}$ in $40 \mathrm{~s}$ . Find its acceleration. A boat slows from $18 \mathrm{~m/s}$ to stop in $6 \mathrm{~s}$ . Find its acceleration.

Studdy Solution

STEP 1

Assumptions1. The initial speed of the train is0 m/s. The final speed of the train is60 m/s3. The time taken for the train to reach this speed is40 s4. The acceleration is constant

STEP 2

The formula for acceleration is given by the change in velocity divided by the time taken for this change. Mathematically, this is represented as $Acceleration = \frac{Final\, speed - Initial\, speed}{Time}$

STEP 3

Now, plug in the given values for the initial speed, final speed, and time into the formula to calculate the acceleration.
$Acceleration = \frac{60\, m/s -0\, m/s}{40\, s}$

STEP 4

Calculate the acceleration.
$Acceleration = \frac{60\, m/s}{40\, s} =1.\, m/s^2$ The acceleration of the train is $1.\, m/s^2$ .

STEP 5

Assumptions for the boat problem1. The initial speed of the boat is18 m/s2. The final speed of the boat is0 m/s (as it comes to a stop)
3. The time taken for the boat to stop is s4. The deceleration (negative acceleration) is constant

STEP 6

We use the same formula for acceleration, but this time the initial speed is greater than the final speed, so the acceleration will be negative (indicating a slowdown or deceleration).
$Acceleration = \frac{Final\, speed - Initial\, speed}{Time}$

STEP 7

Now, plug in the given values for the initial speed, final speed, and time into the formula to calculate the acceleration.
$Acceleration = \frac{0\, m/s -18\, m/s}{6\, s}$

STEP 8

Calculate the acceleration.
$Acceleration = \frac{-18\, m/s}{6\, s} = -3\, m/s^2$ The acceleration (or in this case, deceleration) of the boat is $-3\, m/s^2$ .

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QuestionA train accelerates from rest to 60 m/s60 \mathrm{~m/s}60 m/s in 40 s40 \mathrm{~s}40 s. Find its acceleration. A boat slows from 18 m/s18 \mathrm{~m/s}18 m/s to stop in 6 s6 \mathrm{~s}6 s. Find its acceleration.

Studdy Solution

STEP 1

Assumptions1. The initial speed of the train is0 m/s. The final speed of the train is60 m/s3. The time taken for the train to reach this speed is40 s4. The acceleration is constant

STEP 2

The formula for acceleration is given by the change in velocity divided by the time taken for this change. Mathematically, this is represented asAcceleration=Final speed−Initial speedTimeAcceleration = \frac{Final\, speed - Initial\, speed}{Time}Acceleration=TimeFinalspeed−Initialspeed​

STEP 3

Now, plug in the given values for the initial speed, final speed, and time into the formula to calculate the acceleration.Acceleration=60 m/s−0 m/s40 sAcceleration = \frac{60\, m/s -0\, m/s}{40\, s}Acceleration=40s60m/s−0m/s​

STEP 4

Calculate the acceleration.Acceleration=60 m/s40 s=1. m/s2Acceleration = \frac{60\, m/s}{40\, s} =1.\, m/s^2Acceleration=40s60m/s​=1.m/s2The acceleration of the train is 1. m/s21.\, m/s^21.m/s2.

STEP 5

Assumptions for the boat problem1. The initial speed of the boat is18 m/s2. The final speed of the boat is0 m/s (as it comes to a stop)3. The time taken for the boat to stop is s4. The deceleration (negative acceleration) is constant

STEP 6

STEP 7

Now, plug in the given values for the initial speed, final speed, and time into the formula to calculate the acceleration.Acceleration=0 m/s−18 m/s6 sAcceleration = \frac{0\, m/s -18\, m/s}{6\, s}Acceleration=6s0m/s−18m/s​

STEP 8

Calculate the acceleration.Acceleration=−18 m/s6 s=−3 m/s2Acceleration = \frac{-18\, m/s}{6\, s} = -3\, m/s^2Acceleration=6s−18m/s​=−3m/s2The acceleration (or in this case, deceleration) of the boat is −3 m/s2-3\, m/s^2−3m/s2.

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QuestionA train accelerates from rest to $60 \mathrm{~m/s}$ in $40 \mathrm{~s}$ . Find its acceleration. A boat slows from $18 \mathrm{~m/s}$ to stop in $6 \mathrm{~s}$ . Find its acceleration.

The formula for acceleration is given by the change in velocity divided by the time taken for this change. Mathematically, this is represented as $Acceleration = \frac{Final\, speed - Initial\, speed}{Time}$

Now, plug in the given values for the initial speed, final speed, and time into the formula to calculate the acceleration.
$Acceleration = \frac{60\, m/s -0\, m/s}{40\, s}$

Calculate the acceleration.
$Acceleration = \frac{60\, m/s}{40\, s} =1.\, m/s^2$ The acceleration of the train is $1.\, m/s^2$ .

Assumptions for the boat problem1. The initial speed of the boat is18 m/s2. The final speed of the boat is0 m/s (as it comes to a stop)
3. The time taken for the boat to stop is s4. The deceleration (negative acceleration) is constant

Now, plug in the given values for the initial speed, final speed, and time into the formula to calculate the acceleration.
$Acceleration = \frac{0\, m/s -18\, m/s}{6\, s}$

Calculate the acceleration.
$Acceleration = \frac{-18\, m/s}{6\, s} = -3\, m/s^2$ The acceleration (or in this case, deceleration) of the boat is $-3\, m/s^2$ .