Question

QUESTION 2The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and t in seconds.s = 7t^2 + 2t + 8, 0 ≤ t ≤ 2Find the body's speed and acceleration at the end of the time interval.16 m/sec, 2 m/sec230 m/sec, 28 m/sec238 m/sec, 14 m/sec230 m/sec, 14 m/sec2

Answer 1

Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given function

We were given distance to be:

$s=7t^2+2t+8$

And also time to be:

$0\leq t\leq2$

STEP 2: Find the speed and acceleration at end of time interval

We have to find speed and acceleration at end of time interval means at t = 2 secs. It should be noted that speed is rate of change of distance. So the speed will be the derivative of the equation of distance. The speed will be

$\frac{ds}{dt}=\frac{d(7t^2+2t+8)}{dt}=14t+2$

The speed at t = 2 since it is the end of the time interval will be:

$14(2)+2=28+2=30m\text{ /}sec$

It should be noted that acceleration is rate of change of speed. So the acceleration will be the derivative of the equation of speed. The acceleration will be:

$\frac{d(speed)}{dt}=\frac{d(14t+2)}{dt}=14+0=14$

Hence, the acceleration will be given as 14 m/sec2

Therefore, the answer will be given as:

$30m\text{ /}sec,\text{ }14m\text{ /}sec^2$