Answer :
Answer:
acceleration = 5.21 m/s²
Explanation:
given data
distance d = 100 m
time v = 11.3 s
max speed time u = 1.85 s
to find out
acceleration a
solution
we know initial speed is zero
and after 1.85 s lisa run 11.3 s
so we consider after 1.85 s lisa run at constant speed that is 11.3 - 1.85 = 9.45 s
we consider lisa run with velocity x
so velocity
V = u +at
x = 0 + a(1.85)
a = x / 1.85 m/s² ..................1
and distance travel with x = speed × time
distance at x velocity = 9.45 x ...............2
now calculate the distance to reach at maximum speed by distance formula
distance = ut + 1/2 ×at²
distance = 0 + 1/2 ×(x/1.85)(1.85)²
distance = 0.925 x meters ...................3
so from equation 2 and 3
total distance = 0.925 x + 9.45 x
100 = 0.925 x + 9.45 x
so x = 9.6385 m/s
so from equation 1
a = x / 1.85 m/s²
a = 9.6385 / 1.85 m/s²
a = 5.21 m/s²
Acceleration of a object is the rate of change of velocity of the object per unit time.
The value of the Lisa's acceleration is 5.21 m/s squared.
What is the acceleration of a object?
Acceleration of a object is the rate of change of velocity of the object per unit time.
Given information-
The total distance of the race is 100 m.
Lisa crosses the finish line in 11.3 seconds.
Accelerating uniformly, Lisa took 1.85 s to attain maximum speed.
The distance formula from the second equation of the motion can be given as,
[tex]s=ut+\dfrac{1}{2}at^2[/tex]
Here, [tex]u[/tex] is the initial body, [tex]a[/tex] is the acceleration of the body and [tex]t[/tex] is the time taken by it.
The initial speed is zero.
Let the distance traveled is [tex]x_1[/tex] m.Thus put the value in the above equation as,
[tex]x_1=0+\dfrac{1}{2}at^2\\x_1=\dfrac{1}{2}a(1.85)^2\\[/tex]
Let the above equation as equation 1.
The velocity formula from the first equation of motion can be given as
[tex]v=u+at\\v=0+a\times1.85\\a=\dfrac{v}{(1.85)}[/tex]
Put this value in the above equation 1 as,
[tex]x_1=\dfrac{1}{2}\times\dfrac{v}{1.85} (1.85)^2\\x_1=0.925v[/tex]
The distance traveled with velocity [tex]v[/tex] is,
[tex]x_2=vt\\x_2=9.45v[/tex]
As the total distance is 100 meters. Thus,
[tex]x=x_1+x_2\\100=0.925v+9.45v\\v=9.6385\rm m/s[/tex]
As the acceleration is the ratio of velocity to the time. Thus,
[tex]a=\dfrac{9.6385}{1.85} \\a=5.21\rm m/s^2[/tex]
Hence the value of the Lisa's acceleration is 5.21 m/s squared.
Learn more about the acceleration here;
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