ce amath--- inintegration

1. the slope of a curve at any point (x,y) is 4x-3/2x^2 and the curve passes through (2,5). Find its equation.
dy/dx = 4x - (3/2)x^2
y = 2x^2 - x^3/2 + C, C is constant
5 = 2(2)^2 - 2^3/2 + C, C = 1
y = 2x^2 - x^3/2 + 1
2.At every point on a certain curve, d^2y/dx^2=2(1-x). If it passes through the point (1,3) and the slope is 5 at that point, find the equation of the curcve.
d^2y/dx^2 = 2(1-x)
dy/dx = 2x - x^2 + m, m is constant
2(1) - 1^2 + m = 5, m = 4
dy/dx = 2x - x^2 + 4
y = x^2 - x^3/3 + 4x + n, n is constant
3 = 1^2 - 1^3/3 + 4(1) + n, n = -5/3
y = x^2 - x^3/3 + 4x - 5/3
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3.If a particle starts moving form the starting point at a speed 2m/s with a constant accleration of 10 m/s^2, find the displacement at time t1
s = ut + (1/2)at^2
u = 2 m/s
a = 10 m/s^2
s = displacement
t = time
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