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**differentiate** **1. A particle is projected with an initial velocity of V m/s and attains a maximum height of 12.5m before landing 100m from the point of projection. Calculate the value of V. **

use these three equations, all derived from the basic equations for kinematics w/ constant acceleration.

$\displaystyle v_{oy} = \sqrt{2gh}$

$\displaystyle t = \frac{2v_{oy}}{g}$

$\displaystyle v_x = \frac{\Delta x}{t} $

then ...

$\displaystyle v_o = \sqrt{(v_{oy})^2 + (v_x)^2}$

Can someone check my answer for this?

**2. The displacement, x, of a particle moving in a straight line is represented by the equation: x = 5cos4t**

Find a) The initial velocity of the particle

b) initial acceleration of the particle

a) $\displaystyle x = 5cos4t$

$\displaystyle v = x' = -20sin4t$

initial velocity.. when t = 0, v = 0

b) $\displaystyle a = x" = -80cos4t $

when t =0, a = -80

both correct