Respuesta :
Answer:
The value of t₁ is 5.119 sec.
Explanation:
Given that,
Acceleration = 12.7 m/s²
Total distance [tex]D=5.85\times10^{3}\ m[/tex]
Time = 94.6 sec
We need to calculate the distance
Using equation of motion
[tex]s=ut+\dfrac{1}{2}at^2[/tex]
Put the value into the formula
[tex]s_{1}=0+\dfrac{1}{2}12.7t_{1}^2[/tex]...(I)
We need to calculate the velocity
Using equation of motion
[tex]v=u+at[/tex]
Put the value into the formula
[tex]v=0+12.7t_{1}[/tex]
[tex]v=12.7t_{1}[/tex]
The sled while moves with constant velocity v for time t₂
Using formula of distance
[tex]s_{2}=vt_{2}[/tex]
[tex]s_{2}=12.7t_{1}t_{2}[/tex]
The total distance is
[tex]s_{1}+s_{2}=5.85\times10^{3}[/tex]
Put the value of s₁ and s₂
[tex]\dfrac{1}{2}12.7t_{1}^2+12.7t_{1}t_{2}=5.85\times10^{3}[/tex]
[tex]6.35t_{1}+12.7t_{1}t_{2}=5.85\times10^{3}[/tex]...(II)
The total time is
[tex]t_{1}+t_{2}=94.6[/tex]....(III)
From equation (II) and (III)
After solving
[tex]t_{1}=5.119\ sec[/tex]
Hence, The value of t₁ is 5.119 sec.
