Answer:
0.29[tex]\text{m}\text{s}^{2}[/tex]
Explanation:
Given: Haley is driving down a straight highway at 73 mph. A construction sign warns that the speed limit will drop to 55 mph in 0.50 mi.
To Find: constant acceleration (in [tex]\text{m}\text{s}^{2}[/tex]) that will bring Haley to this lower speed in the distance available
Solution:
we know that,
[tex]1[/tex] mile=[tex]1.609[/tex]km
[tex]1[/tex] km[tex]\setminus[/tex]h = [tex]5\setminus18 m\setminus s[/tex]
Initial Speed of Haley(u)=[tex]73[/tex] mph
[tex]73\times 1.609\times 5\setminus 18[/tex]
[tex]32.63[/tex][tex]\text{m}\setminus\text{s}[/tex]
Final Speed of Haley(v)= [tex]55[/tex] mph
[tex]55\times 1.609\times 5\setminus 18[/tex]
[tex]24.58[/tex][tex]\text{m}\setminus\text{s}[/tex]
The distance to be travelled while lowering the speed(S)=[tex]0.5[/tex] mile
[tex]0.805[/tex] km
[tex]805[/tex] m
according to third equation of motion,
[tex]\text{v}^{2}-\text{u}^{2}=2\text{a}\text{S}[/tex]
as speed is lowering down the acceleration will be in the opposite direction of motion, hence acceleration will be negative, equation will become
[tex]\text{u}^{2} -\text{v}^{2}=2a\text{S}[/tex]
putting values,
[tex]32.63^{2}[/tex]-[tex]24.58^{2}[/tex]=[tex]2a\times805[/tex]
a=[tex]460.55\setminus1610[/tex]
a≅[tex]0.29[/tex][tex]\text{m}\text{s}^{2}[/tex]
the constant acceleration that will drop speed to [tex]55 \text{mph}[/tex] is [tex]0.29[/tex][tex]\text{m}\text{s}^{2}[/tex]
The constant acceleration of the driver is -0.286 m/s²
The given parameters;
initial velocity of the driver, v = 73 mph
final velocity of the driver, v = 55 mph
distance available, d = 0.5 mile
The constant acceleration of the driver is calculated as follows;
[tex]v^2 = u^2 + 2as\\\\2as = v^2 - u^2\\\\a = \frac{v^2 - u^2}{2s} \\\\a = \frac{55^2 - 73^2}{2(0.5)} \\\\a = -2,304\ mi/h^2[/tex]
The acceleration in m/s²
1 mile = 1609 m
[tex]a = \frac{-2304 \ mi}{hr^2} \times \frac{1609 \ m}{1 \ mile} \times \frac{1 \ hr^2}{(3600)^2 \ s^2} \\\\a = -0.286 \ m/s^2[/tex]
Thus, the constant acceleration of the driver is -0.286 m/s²
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