(a) The position of a particle at time t is s(t) = t^3 + t. Compute the average velocity over the time interval [7, 12].(b) Esti

Question

2 years ago

12

mate the instantaneous velocity at t = 7. (Round your answer to the nearest whole number)

1 answer:

ryzh [129] · Answer 1 · 2022-04-02T23:09:11+03:00

Answer:

<h2>a) Average velocity = 278 units</h2><h2>b) Instantaneous velocity at t = 7 seconds is 148 units</h2>

Step-by-step explanation:

a) Average velocity is the ratio of displacement to time.

We have

s(t) = t³ + t

t is in between 7 and 12

s(7) = 7³ + 7 = 350

s(12) = 12³ + 12 = 1740

Displacement = 1740 - 350 = 1390

Time = 12 - 7 = 5

Displacement = Average velocity x time

1390 = Average velocity x 5

Average velocity = 278 units

b) s(t) = t³ + t

Differentiating

v(t) = 3t² + 1

At t = 7

v(t) = 3 x 7² + 1 = 148 units

Instantaneous velocity at t = 7 seconds is 148 units