Question

A rocket starting from its launch pad is subjected to a uniform acceleration of 100 meters/second2. Determine the time needed to reach the final velocity of 1,000 meters/second.

Answer 1

10s

Step-by-step 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:

`v=at+v_o` where "v" is the final velocity at some later time "t", "a" is the constant acceleration, and "v" sub-zero is the initial velocity.

`v=at+v_o`

`(1000\text{ [m/s]})=(100 \text{ } [\text{m/s}^2] )t+(0\text{ [m/s]})`

`1000\text{ [m/s]}=100 \text{ } [\text{m/s}^2] *t`

`\frac{1000\text{ [m/s]}}{100 \text{ } [\text{m/s}^2]}=\frac{100 \text{ } [\text{m/s}^2] *t}{100 \text{ } [\text{m/s}^2]}`

`10\text{ [s]}=t`

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.

Verification:

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=(100 [(m)/(s)])/(1[s])`, 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