Question
Asked Nov 17, 2019
24 views

A particle is moving so that at any time t, its acceleration is 10t for t > or equal to 0. At the end of three seconds, the particle has moved 105 feet. What is its velocity at the end of 3 seconds? 

check_circle

Expert Answer

Step 1

Given that,

The acceleration of the particle is 10t for t ≥ 0.

The particle reached at the distance of 105 feet at t =3 sec.

Step 2

Let s be the distance and v be the velocity at any time t and u be the particle initial velocity.

dv
dt
dv adt
-=f adt
10tdt
V-u 10
2
.....i
help_outline

Image Transcriptionclose

dv dt dv adt -=f adt 10tdt V-u 10 2 .....i

fullscreen
Step 3

Integrate it again using...

ds
dt
ds vdt
105
ds vdt
105
105-05 ut
105 453u
105-45
....ii
u20
help_outline

Image Transcriptionclose

ds dt ds vdt 105 ds vdt 105 105-05 ut 105 453u 105-45 ....ii u20

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus