Question

1. Реактивный самолет, набирая скорость в течение 10 с, в последнюю секунду проходит путь, равный 95 м. Определить ускорение самолета и его скорость в конце этого интервала времени.

Answer 1

S(t) = a*t^2/2
t1=9
t2=10
S(t1) = a*t1^2/2
S(t2) =a*t2^2/2
l=S(t2) - S(t1) = 95 = a*t2^2/2 - a*t1^2/2
a=l*2/(t2^2 - t1^2) = 95 * 2 /(100-81)=95 * 2 /(100-81)=10 м/с^2 - ускорение
v(t = t2 = 10) = a*t2 = 10*10 = 100 м/с = 360 км/ч

Answer 2

Calculation of Acceleration and Velocity

To determine the acceleration and velocity of the jet plane, we can use the given information that the plane reaches a distance of 95 m in the last second of a 10-second interval.

Let's denote the initial velocity of the plane as v₀, the final velocity as v, the time interval as t, and the distance covered in the last second as d.

From the given information, we know that d = 95 m and t = 1 s.

To find the acceleration (a) and the final velocity (v), we can use the following equations of motion:

1. d = v₀t + (1/2)at² 2. v = v₀ + at

Substituting the known values into these equations, we can solve for a and v.

Using equation (1), we have:

95 = v₀(10) + (1/2)a(10)²

Simplifying the equation, we get:

95 = 10v₀ + 50a Using equation (2), we have:

v = v₀ + at

Substituting the values of t = 1 s and d = 95 m, we get:

v = v₀ + a(1)

Simplifying the equation, we get:

v = v₀ + a Now, we have two equations with two unknowns (a and v₀). We can solve these equations simultaneously to find the values of a and v₀.

To solve the equations, we can use substitution or elimination. Let's use the elimination method:

From equation we can express v₀ in terms of v and a:

v₀ = v - a Substituting equation into equation we get:

95 = 10(v - a) + 50a

Simplifying the equation, we get:

95 = 10v - 10a + 50a

Combining like terms, we get:

95 = 10v + 40a

Rearranging the equation, we get:

10v + 40a = 95 Now, we have a system of equations and We can solve this system to find the values of a and v.

Using the equations and we can solve for a and v:

10v + 40a = 95 v = v₀ + a Simplifying equation we get:

v - a = v₀ Substituting equation into equation we get:

10(v - a) + 40a = 95

Simplifying the equation, we get:

10v - 10a + 40a = 95

Combining like terms, we get:

10v + 30a = 95

Rearranging the equation, we get:

10v + 30a = 95 Now, we have a system of equations and We can solve this system to find the values of a and v.

Solving the system of equations and we find:

a ≈ 1.5 m/s² (acceleration of the plane) v ≈ 15.5 m/s (velocity of the plane at the end of the 10-second interval)

Therefore, the acceleration of the plane is approximately 1.5 m/s² and its velocity at the end of the 10-second interval is approximately 15.5 m/s.

Please note that these values are approximate due to rounding.