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Zorluk: OrtaSpeed, Velocity, and Acceleration

A coastal patrol boat is cruising at an initial velocity of 5.0 m/s5.0 \text{ m/s}. The captain orders the engines to increase power, causing the boat to accelerate at a constant rate of 0.2 m/s20.2 \text{ m/s}^2 for exactly 1.5 minutes1.5 \text{ minutes}.

What is the final velocity of the boat in m/s\text{m/s}?

Cevap: 23 m/s

Cevap

23.0
The correct answer is derived by first converting the time from minutes to seconds (1.5 min=90 s1.5 \text{ min} = 90 \text{ s}), calculating the total change in velocity (0.2×90=18.0 m/s0.2 \times 90 = 18.0 \text{ m/s}), and then adding that change to the initial cruising velocity (5.0+18.0=23.0 m/s5.0 + 18.0 = 23.0 \text{ m/s}).

Adım Adım Çözüm

1
Extract and convert the time variable into seconds.
t=1.5 minutes×60 seconds/minute=90 secondst = 1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds}
Acceleration is given in meters per second squared (m/s2\text{m/s}^2), so time must be in seconds to ensure unit consistency.
2
Calculate the total change in velocity during the acceleration phase.
Δv=a×t=0.2 m/s2×90 s=18.0 m/s\Delta v = a \times t = 0.2 \text{ m/s}^2 \times 90 \text{ s} = 18.0 \text{ m/s}
The change in velocity is the product of the constant acceleration and the duration of that acceleration.
3
Add the change in velocity to the initial velocity.
vf=vi+Δv=5.0 m/s+18.0 m/s=23.0 m/sv_f = v_i + \Delta v = 5.0 \text{ m/s} + 18.0 \text{ m/s} = 23.0 \text{ m/s}
The final velocity is the starting velocity plus the amount the velocity increased.

Anahtar Kavram

Applying the constant acceleration formula (vf=vi+atv_f = v_i + at) with necessary unit conversions.
Tahmini Süre:1m 0s
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Konular

Speed, Velocity, and Acceleration

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