(1 point) At a time t seconds after it is thrown up in the...

(1 point) At a time t seconds after it is thrown up in the air, a tomato is at a height (in meters) of f(t) = -4.9t^2 + 35t + 3 m. A. What is the average velocity of the tomato during the first 2 seconds? (Include units.) 25.2m/s B. Find (exactly) the instantaneous velocity of the tomato at t = 2. (Include units.) C. What is the acceleration at t = 2? (Include units.) D. How high does the tomato go? (Include units.) 65.5m E. How long is the tomato in the air? (Include units.)

Transcript

00:01 So here we are given the equation that is f of t which is equals to minus 4 .9 of t raised to the power 2 plus 35 of t plus 3.

00:10 So 3 of m.

00:12 So this equation is given to us where t is in second which is representing the time after it is thrown up in air.

00:20 So in the first part of the question we need to find out the average velocity of tomato during the first two second.

00:27 So here we are given the value of time t that is equals to 2 second.

00:31 So at the value t is equals to 0 the value of f function become equals to 0.

00:36 Plug in to the value from here that is equals to 0 that is we can say that 0 raised to the power 2 minus 4 .9 plus 35 multiplied by the 0 plus 3 of m.

00:49 So the value of f of 0 is equals to 3 m and at the value that is t is equals to 0 the value of f of 2 become equals to minus 4 .9 which is multiplied by the 2 raised to the power 2 plus 35 which is multiplied by the 2 plus 3.

01:07 So this from here is equals to minus 4 .9 multiplied by the 4 plus 70 plus 3.

01:13 Solving the term from here this from here become equals to 53 .4.

01:19 So this is the value of f2.

01:22 Now we need to find out the value of the average velocity.

01:25 So average velocity is equals to the total height which is divided by the total time.

01:32 So this is equals to 53 .4 minus 3 m which is divided by 2.

01:39 Solving the term from here this from here become equals to 26 .2 meter per second.

01:47 So this is the answer to the part a of the question.

01:50 Now in the part b of the question we need to find out the value of the velocity.

01:53 So velocity is given by the formula that is equals to d divided by the dt of f of t.

01:58 So we have to differentiate the function with respect to t.

02:01 So this value from here become equals to minus 4 .9 multiplied by the 2 of t plus 3 .5 is 35 multiplied by the 1 plus 0.

02:10 So plugging to the value we are considering the velocity at time t is equals to 0...

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