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## Homework Statement

A toy rocket is projected vertically upwards from rest and it rises with an acceleration of (9-5t)g m / s^2 for the first two seconds and, thereafter, freely against gravity. Find: the maximum speed and the maximum height.

## Homework Equations

a = (9-5t)g for the first 2 seconds.

general motion equations

## The Attempt at a Solution

The acceleration after 2 seconds is (9 - 10). -g = 9.81 m/s^2.

The velocity at this point is:

v = u + at

v = 0 + 9.81 x 2 = 19.62 m/s.

Max height occurs when v = 0 therefore ;

0 = 19.62 -9.81 x t

t is = 2, which gives a total time of 4 seconds.

I can get the the max height and velocity easily from here. Except the answers are quite bigger than what I'm getting. So I'm thinking I'm doing something wrong for these first 2 seconds. I don't think I can integrate the acceleration to find velocity because I don't have enough information.

Any help is appreciated :)

Noir