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## Homework Statement

The acceleration of a particle is directly proportional to time, t. At t = 0, the velocity of that particle, v, = 16 in./sec. Knowing that v = 15 in/sec and x = 20in when t = 1, determine the velocity, acceleration and position at x = 7.

## Homework Equations

## The Attempt at a Solution

I took

[tex]\frac{dv}{dt} = kt, so \: v = \frac{k}{2}t^2 + C[/tex]

Solving for C:

[tex]16 = \frac{k}{2}(0)^2 + C[/tex]

C = 16

Solve for k

[tex]1 = \frac{k}{2}(1)^2 + 16[/tex]

k = -30

Therefore:

[tex]v(t) = \-15*(t)^2 + 16[/tex]

This is already wrong; v(7) = -719 in/sec but the book states the answer is -33 in/sec

Any advice on what's gone wrong would be greatly appreciated; this is a revision question too...

Cheers,

Adrian