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## Homework Statement

*A body of mass 5 kg is acted on by a force in a straight line. The magnitude of the force after*

**t**seconds is given by (2t - 3t^2) kg wt. If the body has an initial velocity of 3ms-1 in the same direction as the force, calculate its velocity after 4 seconds.## Homework Equations

∑F = ma

a = dV/dt

## The Attempt at a Solution

So what I've done is this.

m = 5

F = (2t - 3t^2)

a = (2t - 3t^2) / 5

dV/dt = (2t - 3t^2) / 5

v = ∫(2t - 3t^2) / 5 dt

v = (t^2 - t^3) / 5 + c

Using t = 0, v = 3 (from initial velocity), solving for c yields c = 3. So,

v = (t^2 - t^3)/5 + 3 and substituting t = 4, I get v =

**-6.6ms-1**

The back of my textbook gives an answer of

**-91.08ms-1**, could someone please tell me where I've gone wrong?