Answer:
10s
Explanation:
Acceleration is a measure of a rate of change of velocity, or in other words, a measure of how quickly the velocity is changing.
If acceleration is constant, then the velocity is changing by a constant amount.
With an acceleration of 100 m/s^2, starting from the launching pad (and thus, an initial velocity of zero), we can calculate how long it will take to reach a final velocity of 1000m/s with the following formula:
where "v" is the final velocity at some later time "t", "a" is the constant acceleration, and "v" sub-zero is the initial velocity.
![(1000\text{ [m/s]})=(100 \text{ } [\text{m/s}^2] )t+(0\text{ [m/s]})](https://tex.z-dn.net/?f=%281000%5Ctext%7B%20%5Bm%2Fs%5D%7D%29%3D%28100%20%5Ctext%7B%20%7D%20%5B%5Ctext%7Bm%2Fs%7D%5E2%5D%20%29t%2B%280%5Ctext%7B%20%5Bm%2Fs%5D%7D%29)
![1000\text{ [m/s]}=100 \text{ } [\text{m/s}^2] *t](https://tex.z-dn.net/?f=1000%5Ctext%7B%20%5Bm%2Fs%5D%7D%3D100%20%5Ctext%7B%20%7D%20%5B%5Ctext%7Bm%2Fs%7D%5E2%5D%20%2At)
![\dfrac{1000\text{ [m/s]}}{100 \text{ } [\text{m/s}^2]}=\dfrac{100 \text{ } [\text{m/s}^2] *t}{100 \text{ } [\text{m/s}^2]}](https://tex.z-dn.net/?f=%5Cdfrac%7B1000%5Ctext%7B%20%5Bm%2Fs%5D%7D%7D%7B100%20%5Ctext%7B%20%7D%20%5B%5Ctext%7Bm%2Fs%7D%5E2%5D%7D%3D%5Cdfrac%7B100%20%5Ctext%7B%20%7D%20%5B%5Ctext%7Bm%2Fs%7D%5E2%5D%20%2At%7D%7B100%20%5Ctext%7B%20%7D%20%5B%5Ctext%7Bm%2Fs%7D%5E2%5D%7D)
![10\text{ [s]}=t](https://tex.z-dn.net/?f=10%5Ctext%7B%20%5Bs%5D%7D%3Dt)
So, it will take 10 seconds for the rocket to reach 1000m/s when starting from the launching pad, with a constant velocity of 100m/s^2.
<u>Verification:</u>
In this situation, it is quick to verify that 10 seconds is correct by looking at what the velocities will be each second.
Recognizing that the acceleration is ![a=\dfrac{100 [\frac{m}{s}]}{1[s]}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B100%20%5B%5Cfrac%7Bm%7D%7Bs%7D%5D%7D%7B1%5Bs%5D%7D)
, the velocity increases by 100 units [m/s] every second.
At time 0[s], the velocity is 0[m/s]
At time 1[s], the velocity is 100[m/s]
At time 2[s], the velocity is 200[m/s]
At time 3[s], the velocity is 300[m/s]
At time 4[s], the velocity is 400[m/s]
At time 5[s], the velocity is 500[m/s]
At time 6[s], the velocity is 600[m/s]
At time 7[s], the velocity is 700[m/s]
At time 8[s], the velocity is 800[m/s]
At time 9[s], the velocity is 900[m/s]
At time 10[s], the velocity is 1000[m/s]
So, indeed, after 10 seconds, the velocity reaches 1000 m/s
