Force, Mass, and Motion

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An aircraft carrier's munitions elevator is used to transport heavy ordnance to the flight deck. The elevator starts from a complete stop and accelerates upward at a constant rate of $0.5 \text{ m/s}^2$ . How many seconds will it take for the elevator to reach its maximum operational upward velocity of $120 \text{ meters per minute}$ ?

240

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Cevap: 4

Cevap

To find the elapsed time, the units must first be standardized. Since acceleration is given in meters per second squared (

0.5 \text{ m/s}^2

), the target velocity must be converted from meters per minute to meters per second by dividing by 60. This gives a final velocity of

2 \text{ m/s}

. Using the formula for time (

t = \frac{\Delta v}{a}

), dividing

2 \text{ m/s}

0.5 \text{ m/s}^2

results in exactly 4 seconds.

Adım Adım Çözüm

Identify the given variables and the unknown.

Initial velocity (

v_i

) =

0 \text{ m/s}

. Acceleration (

a

) =

0.5 \text{ m/s}^2

. Final velocity (

v_f

) =

120 \text{ m/min}

. Unknown is time (

t

Establishing the known kinematic values is the first step in solving acceleration problems.

Convert the final velocity into standard units (meters per second) to match the acceleration unit.

120 \text{ m/min} \div 60 \text{ s/min} = 2 \text{ m/s}

All units must be consistent before applying mathematical formulas.

Apply the acceleration formula

a = \frac{v_f - v_i}{t}

and solve for

t

0.5 = \frac{2 - 0}{t}

, which rearranges to

t = \frac{2}{0.5} = 4 \text{ seconds}

This calculates the elapsed time required to achieve the desired change in velocity.

Anahtar Kavram

Kinematic equations and unit conversion for acceleration.

Tahmini Süre:1m 0s

Soru 142Soru →

A rapid transit commuter train leaves a station, accelerating uniformly along a straight track. It reaches a cruising velocity of $27.0 \text{ m/s}$ from a complete stop. If the acceleration phase lasts exactly $0.75 \text{ minutes}$ , what is the train's average acceleration in $\text{m/s}^2$ ?

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Cevap: 0.6

Cevap

The train's average acceleration is

0.6 \text{ m/s}^2

Acceleration is defined as the change in velocity divided by the time it takes for that change to occur. By converting the time unit to seconds and substituting the initial velocity, final velocity, and time into the standard acceleration formula, the correct magnitude of

0.6 \text{ m/s}^2

is determined.

Adım Adım Çözüm

Identify the known kinematic variables.

Initial velocity

v_i = 0 \text{ m/s}

, final velocity

v_f = 27.0 \text{ m/s}

, and time

t = 0.75 \text{ minutes}

Extracting the given values is necessary before selecting the appropriate formula.

Convert the time from minutes to standard SI units (seconds).

t = 0.75 \times 60 = 45 \text{ seconds}

Acceleration in

\text{m/s}^2

requires the time unit to match the time component of the velocity unit (seconds).

Calculate the average acceleration using the formula

a = \frac{v_f - v_i}{t}

a = \frac{27.0 - 0}{45} = 0.6 \text{ m/s}^2

This formula directly relates the change in an object's velocity to the time interval over which the change occurred.

Anahtar Kavram

Kinematics: Uniform Acceleration and Unit Conversion

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Force, Mass, and Motion

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