Answer:
-time it takes for the sled to come to a stop after launch of rocket = 7.244 s
-distance sled has travelled from its starting point by the time it finally comes to rest is = 234.8655 m
Explanation:
From the question, looking at the motion while accelerating, we have;
Initial velocity; u = 0 m/s
Acceleration; a = 13.5 m/s²
Time; t = 3.3 s
Let's use first equation of motion to find final velocity (v).
v = u + at
v = 0 + (13.5 × 3.3)
v = 44.55 m/s
In this forward direction, let's calculate the displacement(d1) using newton's 3rd equation of motion.
d1 = ut + ½at²
d1 = 0(3.3) + ½(13.5 × 3.3²)
d1 = 73.5075 m
Now, let's consider the motion while slowing down and our final velocity will be 0 m/s while initial velocity will now be 44.55 m/s while acceleration is 6.15 m/s².
Thus, from v = u + at, we can find the time it take for the sled to come to a stop.
Now, since it's coming to rest acceleration will be negative. Thus;
0 = 44.55 + (-6.15t)
0 = 44.55 - 6.15t
t = 44.55/6.15
t = 7.244 s
Now we want to find out how far the sled has travelled from its starting point by the time it finally comes to rest.
Thus, we'll use the equation;
v² = u² + 2as
Where s will be the second displacement which we will call d2.
Thus;
0² = 44.55² + (-2 × 6.15 × s)
0 = 1984.7025 - 12.3s
12.3s = 1984.7025
s = 1984.7025/12.3
s = 161.358
Thus, d2 = s = 161.358 m
Thus, distance sled has travelled from its starting point by the time it finally comes to rest is ;
= d1 + d2 = 73.5075 + 161.358 = 234.8655 m
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