Answer:
Time : <u>7.96 s</u>
Distance Traveled : <u>357.8 m</u>
Explanation:
In order to solve this problem, we first consider the accelerated motion of rocket. We will be using the subscript 1 for accelerated motion.
So, for accelerated motion, we have:
Acceleration = a₁ = 14.5 m/s²
Time Period = t₁ = 3.1 s
Initial Velocity = Vi₁ = 0 m/s (Since, it starts from rest)
Final Velocity = Vf₁
Distance covered by sled during acceleration motion = s₁
Now, using 1st equation of motion:
Vf₁ = Vi₁ + (a₁)(t₁)
Vf₁ = 0 m/s + (14.5 m/s²)(3.1 s)
Vf₁ = 44.95 m/s
Now, using 2nd equation of motion:
s₁ = (Vi₁)(t) + (0.5)(a₁)(t₁)
s₁ = (0 m/s)(3.1 s) + (0.5)(14.5 m/s²)(3.1 s)
s₁ = 22.5 m
Now, we first consider the decelerated motion of rocket. We will be using the subscript 2 for decelerated motion.
So, for accelerated motion, we have:
Deceleration = a₂ = - 5.65 m/s²
Time Period = t₂ = ?
Initial Velocity = Vi₂ = Vf₁ = 44.95 m/s (Since, decelerate motion starts, where accelerated motion ends)
Final Velocity = Vf₂ = 0 m/s (Since, rocket will eventually stop)
Distance covered by sled during deceleration motion = s₂
Now, using 1st equation of motion:
Vf₂ = Vi₂ + (a₂)(t₂)
0 m/s = 44.95 m/s + (- 5.65 m/s²)(t₂)
t₂ = (44.95 m/s)/(5.65 m/s²)
<u>t₂ = 7.96 s</u>
Now, using 2nd equation of motion:
s₂ = (Vi₂)(t₂) + (0.5)(a₂)(t₂)
s₂ = (44.95 m/s)(7.96 s) + (0.5)(- 5.65 m/s²)(7.96 s)
s₂ = 357.8 m - 22.5 m
s₂ = 335.3 m
Thus, the total distance covered by sled will be:
Total Dustance = S = s₁ + s₂
S = 22.5 m + 335.3 m
<u>S = 357.8 m</u>
