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adelina 88 [10]
4 years ago
10

A car is traveling with a constant speed when the driver suddenly applies the brakes, giving the 14) car a deceleration of 3.50

m/s2. if the car comes to a stop in a distance of 30.0 m, what was the car's original speed?
Physics
1 answer:
sergij07 [2.7K]4 years ago
7 0
To be able to determine the original speed of the car, we use kinematic equations to relate the acceleration, distance and the original speed of the car moving. 

First, we manipulate the one of the kinematic equations
 
v^2 = v0^2 + 2 (a) (x)  where v = 0 since the car stopped

Writing the equation in such a way that the initial velocity or v0 is written on one side of the equation,

<span>we get v0 = sqrt (2(a)(x))

Substituting the known values,

v0 = sqrt(2(3.50)(30.0))
v0 = 14.49 m/s 
</span>
Therefore, before stopping the car the original speed of the car would be 14.49 m/s
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A car initially traveling at 17.1 mph comes to rest in 9.7s what was its acceleration in this time?
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Δv=at

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  • a is the acceleration of the object during this time.
  • t is time

(v_f-v_i)=at is another way to write this equation.

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  • I rearranged this equation to solve for a, but this is a step that you don't need to take, it's just good to get in the habit of doing this.
  • Plug in the given values. Note that our final velocity is 0, because the car travels until at <em>rest</em>.

a=\frac{v_f-v_i}{t}\\a=\frac{(0)-[(17.1\frac{miles}{hour} )(\frac{hour}{3600s})(\frac{1609.34m}{mile})]}{9.7s}

  • Our initial velocity is in mph, something not in standard units, so if not changed, you will get an incorrect answer. What you need to do is cancel out the units your prior value had using division and multiplication, and at the same time multiply and divide the correct numbers and units into your equation. Or look up a converter.

a=\frac{(0)-[(17.1\frac{miles}{hour} )(\frac{hour}{3600s})(\frac{1609.34m}{mile})]}{9.7s}\\a=\frac{0m/s-7.6m/s}{9.7s} \\a=\frac{-7.6m/s}{9.7s}

  • if you converted correctly, your answer for v_f will be ≅ 7.6m/s.
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