When Gorix escaped from Dr. Sloth's ship, his ship started at rest. Gorix immediately set his thrusters to full power, and his ship's acceleration increased by 2 m/s2 every second for 15 seconds. At that point, the ship remained at constant acceleration for another 30 seconds, after which the thrusters powered off, effectively setting his acceleration to zero. Disregarding any other forces acting on the ship, how far did Gorix's ship travel after one minute?
a=2m/s^2 for 15s
then a=0 for another 30 s
For the first 15s would v=at
=(2m/s^2)(15s)=15m/s
how would I solve for d?
I also don't get how I would do the other half of the problem so that I know the distance after one minute.
To find the distance traveled by Gorix's ship after one minute, we can break down the problem into three parts:
1. Calculate the distance traveled during the first 15 seconds when the ship's acceleration is 2 m/s².
2. Calculate the distance traveled during the next 30 seconds when the ship's acceleration is zero.
3. Sum up the distances from steps 1 and 2 to get the total distance traveled.
Let's solve each step:
Step 1: Calculating the distance traveled with constant acceleration of 2 m/s² for 15 seconds.
To find the distance (d) covered during this time, you can use the equation of motion: d = ut + (1/2)at². In this case, the initial velocity (u) is zero because the ship was at rest.
d = 0 * 15 + (1/2) * (2 m/s²) * (15s)²
d = 0 + 0.5 * 2 * 225
d = 0 + 225
d = 225 meters
So, during the first 15 seconds, the ship traveled 225 meters.
Step 2: Calculating the distance traveled with zero acceleration for 30 seconds.
Since the acceleration is zero during this time, the ship maintains a constant velocity equal to the final velocity achieved in Step 1, which was 15 m/s. Therefore, the distance traveled (d) can be calculated using the equation: d = vt.
d = 15 m/s * 30s
d = 450 meters
So, during the next 30 seconds, the ship traveled an additional 450 meters.
Step 3: Calculating the total distance traveled after one minute.
To find the total distance traveled, we add up the distances calculated in Step 1 and Step 2.
Total distance = Distance in Step 1 + Distance in Step 2
Total distance = 225 meters + 450 meters
Total distance = 675 meters
Therefore, after one minute, Gorix's ship traveled a total distance of 675 meters.