A drag racer accelerates at a(t) = 90 ft/s^2. Assume that...

A drag racer accelerates at a(t) = 90 ft/s^2. Assume that v(0) = 0 and s(0) = 0. a. Determine and graph the position function for t ? 0. b. How far does the racer travel in the first 6 s? c. At this rate, how long will it take the racer to travel 1/3 mi? d. How long will it take the racer to travel 300 ft? e. How far has the racer traveled when it reaches a speed of 167 ft/s? a. The position function for t ? 0 is s(t) =

Transcript

0:00 Hi there.

00:01 So for this problem we are told that a drag racer accelerates with an acceleration that is constant and that acceleration is 90 feet per second square.

00:17 So we need to assume that the initial speed is equal to zero and also its initial position is equal to zero.

00:29 So for part a of this problem, we need to determine and graph the position function for the time greater or equal than zero.

00:42 So we know that in this case, the only thing that we have is a positive acceleration.

00:56 So we need to graph the position with respect to the time.

01:01 Now we can see we are given.

01:04 That it starts at zero, so it starts here at the origin.

01:09 And then because the acceleration is positive, it's going to be a graph of this form.

01:16 And this is because the acceleration is greater than zero.

01:21 So that's a solution for part a of this problem.

01:26 Now for part b, we are asked about how far does the razor travel in the first six seconds? so for that we need first to obtain.

01:47 So we know that the position is the position in this case is just going to be given by the initial position, which we know is zero.

02:05 And this times the speed, the initial speed that we also know it is also equal to zero.

02:13 And this time and this a term that is related by the assessment.

02:19 We know that there is 1 divided by 2 times the acceleration times the time square.

02:24 So we substitute the acceleration that we have in here, which is 90 feet per second square.

02:36 And this times the time square.

02:39 So we need to answer the question of how far does the race of travel in the first six seconds? so we just need to evaluate this function at 6 seconds.

02:51 That will be 1 divided by 2 times 90 feet per second.

02:58 That times the times 6 seconds to the square.

03:03 So from this we obtain a value of 1 ,620 feet.

03:16 So that's a solution for part b of this problem.

03:20 Now for part c, we are asked about, now, at this rate, how long will it take the razor to travel 1 divided by 3 miles? so in this case, the distance travel that we are given in this case at the time that we need to determine is 1 divided by 3 miles.

03:52 Now we need to pass this into feet.

03:55 So what we can do is to multiply this by a factor of conversion...

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