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Pie
3 years ago
7

A ball moves in a straight line has an acceleration of a(t) = 2t + 5. Find the position function of the ball if its initial velo

city is -3 cm per second and it’s initial position is 12 cm.
Mathematics
1 answer:
Vlad1618 [11]3 years ago
4 0

Answer:

s(t) = frac{t^3}{3} + \frac{5t^2}{2} - 3t + 12

Step-by-step explanation:

Relation between acceleration, velocity and position:

The velocity function is the integral of the acceleration function.

The position function is the integral of the velocity function.

Acceleration:

As given by the problem, the acceleration function is a(t) = 2t + 5

Velocity:

v(t) = \int a(t) dt = \int (2t+5) dt = \frac{2t^2}{2} + 5t + K = t^2 + 5t + K

In which K is the constant of integration, which is the initial velocity. So K = -3 and:

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

Position:

s(t) = \int v(t) dt = \int (t^2 + 5t - 3) = \frac{t^3}{3} + \frac{5t^2}{2} - 3t + K

In which K, the constant of integration, is the initial position. Since it is 12:

s(t) = frac{t^3}{3} + \frac{5t^2}{2} - 3t + 12

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