The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line.

Question

The acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving along a line.

a(t) = 2t + 6,    v(0) = −16,    0 ≤ t ≤ 5

(a) Find the velocity at time t.

v(t)=______ m/s

(b)Find the distance traveled during the given time interval.

=________ m

Answer 1

Given acceleration is a(t) = 2t + 6 m/s²

a) for velocity we integrate it one times

than v(t)=2t²/2+6t+c=t² +6t+c m/s

where c is some constant which can be find using value of velocity.

So put t=0 and v=-16

-16=c

so v(t)=t²+6t-16 m/s

b) For distance traveled integrate once more

_0∫⁵v(t)=[t³/3+3t²-16t]⁵₀

=125/3+75-80=36.67m