contestada

If a car is traveling 100 km/h west and comes to a stop in 3 min, what is the car's acceleration?

0.15 m/s2 east


0.15 m/s2 west


0.56 m/s2 east


0.56 m/s2 west

Respuesta :

namordu

Answer:

0.15 m/s² east

Explanation:

We can use following kinematic equation for Uniformly-Accelerated Motion to solve this problem:

v = v₀ + a × t

Where v is the final velocity, v₀ is the initial velocity, a is the acceleration and t is the time interval.

The data of the problem is:

  • v₀ = - 100km/h (remember to have a frame of reference, I decided traveling west will be towards the negative values and traveling east will be positive).
  • v = 0 km/h (the car comes to a full stop)
  • t = 3 min

Replacing the data in the formula:

0 km/h = -100 km/h + a × 3 min

It's very important to use the same units when solving problems. I will convert kilometer to meters and hour or minutes to seconds, because the answer choices are given in m/s².

  • 0 km/h = 0 m/s
  • [tex]\frac{100 \ km}{\ \ h} * \frac{1000\ m}{1\ km} * \frac{1\ \ h}{3600\ s} = \frac{27.78\ m}{\ \ \ \ s}[/tex]
  • [tex]3 min * \frac{60\ s}{1\ m} = 180 s[/tex]

Then:

[tex] 0 m/s = -27.78 \ m/s + a * 180 s\\+27.78 m/s = a * 180 s\\[/tex]

[tex]\frac{+27.78 \ m/s}{180\ s} = a\\\\+ 0.15 m/s^2 = a[/tex]

And considering our frame of reference, a positive sign indicates that the acceleration is east-bound.

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