math calculus 2

Question

The acceleration function (in m/s2m/s2) and initial velocity for a particle moving along a line is given by 

a(t)=2t+8,v(0)=10,0≤t≤10.a(t)=2t+8,v(0)=10,0≤t≤10.

(a) Find the velocity (in m/s) of the particle at time tt. 

Velocity =   meters

(b) Find the total distance traveled (in meters) by the particle. 

Total distance traveled =   meters

Answer 1

dv = adt integral from v(0) to v(t) of dv = integral from 0 to t of adt or (2t + 8)dt

v - v(0) = t² + 8t v = t² + 8t + 10 m/s

I hate that calculus books throw in speed and distance into these calculations!

Strictly, displacement or x - x(0) = integral from 0 to 10 of vdt.

This integral is only equal to the distance if |vdt| is calculated. For this problem, the velocity is positive-definite, so we can write

distance = integral from 0 to t of vdt.

I'll leave that to you to integrate. .