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Difficulty: MediumSpeed, Velocity, and Acceleration

Determine the acceleration for each of the military transport operations described below. Sequence the operations from the lowest rate of acceleration to the highest.

  1. 1A naval destroyer accelerating from 5 m/s5 \text{ m/s} to 15 m/s15 \text{ m/s} in 20 seconds20 \text{ seconds}
  2. 2An armored personnel carrier increasing its speed from 10 m/s10 \text{ m/s} to 22 m/s22 \text{ m/s} in 6 seconds6 \text{ seconds}
  3. 3A transport plane accelerating from rest to 60 m/s60 \text{ m/s} in 15 seconds15 \text{ seconds}
  4. 4A rescue helicopter accelerating from rest to 45 m/s45 \text{ m/s} in 9 seconds9 \text{ seconds}

Answer

The correct order from lowest to highest acceleration is: Naval destroyer, Armored personnel carrier, Transport plane, and Rescue helicopter.
By systematically calculating the acceleration for each scenario using the formula a=vf−vita = \frac{v_f - v_i}{t}, we can determine their respective values and order them properly. The naval destroyer evaluates to 0.5 m/s20.5 \text{ m/s}^2, the armored personnel carrier evaluates to 2.0 m/s22.0 \text{ m/s}^2, the transport plane evaluates to 4.0 m/s24.0 \text{ m/s}^2, and the rescue helicopter evaluates to 5.0 m/s25.0 \text{ m/s}^2. Placing these in ascending order yields the correct sequence.

Step-by-Step Solution

1
Calculate the acceleration of the naval destroyer.
a=15−520=0.5 m/s2a = \frac{15 - 5}{20} = 0.5 \text{ m/s}^2
Using the formula a=vf−vita = \frac{v_f - v_i}{t}
2
Calculate the acceleration of the armored personnel carrier.
a=22−106=2.0 m/s2a = \frac{22 - 10}{6} = 2.0 \text{ m/s}^2
Using the formula a=vf−vita = \frac{v_f - v_i}{t}
3
Calculate the acceleration of the transport plane.
a=60−015=4.0 m/s2a = \frac{60 - 0}{15} = 4.0 \text{ m/s}^2
Using the formula a=vf−vita = \frac{v_f - v_i}{t}, remembering that 'from rest' means an initial velocity of 0 m/s0 \text{ m/s}
4
Calculate the acceleration of the rescue helicopter.
a=45−09=5.0 m/s2a = \frac{45 - 0}{9} = 5.0 \text{ m/s}^2
Using the formula a=vf−vita = \frac{v_f - v_i}{t}, remembering that 'from rest' means an initial velocity of 0 m/s0 \text{ m/s}
5
Sequence the vehicles by their calculated acceleration values from lowest to highest.
0.5<2.0<4.0<5.00.5 < 2.0 < 4.0 < 5.0
To satisfy the condition of ordering from lowest rate to highest rate.

Key Concept

Acceleration is the rate of change of velocity over time, calculated using the formula a=vf−vita = \frac{v_f - v_i}{t}.
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Topics

Speed, Velocity, and Acceleration

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