Math  /  Algebra

QuestionChallenge: A 3 kg model airplane is traveling at a speed of 33 m/s. The operator then increases the speed up to 45 m/s in 2 seconds. How much force did the engine need in order to make this change?

Studdy Solution

STEP 1

1. The mass of the model airplane is 3 kg.
2. The initial speed of the airplane is 33 m/s.
3. The final speed of the airplane is 45 m/s.
4. The time taken to change the speed is 2 seconds.
5. We are trying to find the force exerted by the engine.

STEP 2

1. Calculate the change in velocity.
2. Calculate the acceleration.
3. Use Newton's second law to find the force.

STEP 3

Calculate the change in velocity.
The change in velocity (Δv \Delta v ) is given by the difference between the final velocity (vf v_f ) and the initial velocity (vi v_i ):
Δv=vfvi \Delta v = v_f - v_i Δv=45m/s33m/s \Delta v = 45 \, \text{m/s} - 33 \, \text{m/s} Δv=12m/s \Delta v = 12 \, \text{m/s}

STEP 4

Calculate the acceleration.
Acceleration (a a ) is the change in velocity divided by the time taken (t t ):
a=Δvt a = \frac{\Delta v}{t} a=12m/s2s a = \frac{12 \, \text{m/s}}{2 \, \text{s}} a=6m/s2 a = 6 \, \text{m/s}^2

STEP 5

Use Newton's second law to find the force.
Newton's second law states that force (F F ) is the product of mass (m m ) and acceleration (a a ):
F=m×a F = m \times a F=3kg×6m/s2 F = 3 \, \text{kg} \times 6 \, \text{m/s}^2 F=18N F = 18 \, \text{N}
The force exerted by the engine is:
18N \boxed{18 \, \text{N}}

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