Question

Санки, скатывающиеся с горы, в первые три секунды проходят 2м, а в последующие три секунды-4м. Считая движение равноускоренным, найдите ускорение и начальную скорость санок

Answer 1

S1=2; S2=2+4=6; t1=3; t2=3+3=6;
S1=v0*t1+(at1^2)/2; S2=v0*t2+(at2^2)/2;
или 2S1=2v0t1+at1^2; 2S2=2v0t2+at2^2; выражаем 
v0=(2S1-at1^2)/2t1; v0=(2S2-at2^2)/2t2;  уравниваем правые части и используем правило пропорции,  
(2S1-at1^2)*2t2=2t1*(2S2-at2^2); 2 сокращаем и получаем 
2S1t2-at1^2t2=2S2t1-at2^2t1;  at2^2t1-at1^2t2=2S2t1-2S1t2;
a(t2^2t1-t1^2t2)=2S2t1-2S1t2;  a*(36*3-9*6)=2*6*3-2*2*6;
a*54=12; a=12/54=2/9;
v0=(S1-at1^2)/t1;  v0=(2-2)/3=0

Answer 2

Calculating Acceleration and Initial Velocity of the Sled

To find the acceleration and initial velocity of the sled, we can use the equations of motion for uniformly accelerated motion. The equations are:

1. Final velocity \(v\) = Initial velocity \(u\) + Acceleration \(a\) * Time \(t\) 2. Distance traveled \(s\) = Initial velocity \(u\) * Time \(t\) + 0.5 * Acceleration \(a\) * Time \(t\)\(^2\) 3. \(v\)\(^2\) = \(u\)\(^2\) + 2 * \(a\) * \(s\)

Given: - Distance traveled in the first 3 seconds, \(s_1\) = 2m - Distance traveled in the subsequent 3 seconds, \(s_2\) = 4m - Total time, \(t\) = 6 seconds

We can use these equations to find the acceleration and initial velocity of the sled.

Calculating Acceleration

Using the second equation, we can find the acceleration \(a\) using the distance traveled in the first 3 seconds: \[s_1 = u * t + 0.5 * a * t^2\]

Calculating Initial Velocity

We can find the initial velocity \(u\) using the first equation: \[v = u + a * t\]

Let's calculate the acceleration and initial velocity using the given information.

Solution

Using the given distances and time, we can calculate the acceleration and initial velocity of the sled.

Step 1: Calculating Acceleration \[2 = u * 3 + 0.5 * a * 3^2\] \[4 = u * 3 + 0.5 * a * 3^2\]

Step 2: Calculating Initial Velocity \[v = u + a * t\]

Conclusion

By solving the above equations, we can find the values of acceleration and initial velocity for the sled.