Particle Motion; Acceleration directly proportional to time

[Alexanddros81]

Homework Statement

11.10 The acceleration of a particle is directly proposional to the time t.
At t = 0, the velocity of the particle is v = 16 in./s. Knowing that v = 15 in./s
and that x = 20 in. when t = 1 s, determine the velocity, the position, and
the total distance traveled when t = 7s.

Homework Equations

The Attempt at a Solution

totally confused on this one; Any hints?

 

[PeroK]

The acceleration depends on time in this problem. You need to use that information.

 

[Alexanddros81]

Hi!
Is the following correct?

$v-v_0 = \int_0^1 a \, dt + C1$
$v-v_0 = \int_0^1 f(t) \, dt + C1$
Since a is directly propotional to t it follows that
$v-v_0 = \int_0^1 t \, dt + C1$
$v-v_0 = \left[ \frac {t^2} {2} \right]_0^1 + C1$
$v-v_0 = \frac {1} {2} + C1$
$15-16 = \frac {1} {2} + C1 \Rightarrow C1 = -\frac {3} {2}$

Is $a = -1 \frac {in} {s^2}$ as I have calculated on my first post?