1 distance is in meters and time is in seconds a rocket...

Distance is in meters and time is in seconds. A rocket flies vertically upwards. At time t=1, the rocket is 95 m above the ground and is moving upwards with a speed of 70 m/s. The acceleration of the rocket at time t is 6t+2 m/s^2 upwards. a. What is the velocity at time t? m/s b. What is the height of the rocket at time t? c. What is the average velocity between t=0 and t=2? m/s

Transcript

00:01 For this question, we are looking at the trajectory of a rocket flying vertically upwards.

00:07 We are given the acceleration of the rocket as a function of t, and it is 6t, a little messy, 6t plus 2 meters per second squared at all times t.

00:26 Now, remember that this is equal to the derivative of velocity as well.

00:36 Or the second derivative of position with respect to t.

00:49 And we are also given the data that at t equals 1, we have that v of 1 is equal to 70 meters per second squared, or per second, sorry, and h of 1, the height, is equal to 95 meters.

01:11 So with this data, we should be able to answer the question.

01:17 So let's look at part a.

01:22 Part a asks us what the velocity of the rocket is at time t.

01:27 Well, we know that the acceleration, which is the derivative of the velocity, is equal to 6t plus 2.

01:37 So we just need to integrate this.

01:40 So v of t is equal to we use the power rule to integrate this.

01:47 So you add one to the power, divide by the new power.

01:50 So in this case, the power is one.

01:52 We add one to that and get two.

01:54 So we divide by two and get a three here.

01:57 And we have to add one of the power.

01:58 So we get three t squared for this term.