Question

The function sequals​f(t) gives the position of a body moving on a coordinate​ line, with s in meters and t in seconds. Find the​ body's displacement and average velocity for the given time interval. sequals6t squaredplus3tplus5​, 0 less than or equalsxless than or equals2

Answer 1

Δs=10m

`v_a_v=`5m/s

Explanation:

s=t²+3t +5,0<=t<=2

Let f(t)=s=t²+3t +5

The displacement of the body over the time interval from 0 to 2 is

Δs=f(2)-f(0)

Δs=(2²+3(2) +5) - (0²+3(0) +5)

Δs=10m

The average velocity of the body over the time interval from 0 to 2 is

`v_a_v=`displacement / travel time =Δs/Δt

=10 / 2

=5m/s