Question

A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 7, s(0) = 5, v(0) = −8 s(t) =

Answer 1

`s_(_t_)=(1)/(3)t^3+(7)/(2)t^2-8t+5`

Explanation:

1.)

`a_t=v'_t\\v_t=\int(a_(_t_)dt\\v_t=\int(2t+7)dt\\v_t=t^2+7t+C\\`

2.)

`v_0=-8\\-8=(0)^2+7(0)+C\\C=-8\\v_t=t^2+7t-8`

3.)

`v_t=s'_t\\s_t=\int(v_t)dt\\s_t=\int(t^2+7t-8)dt\\s_t=(1)/(3)t^3+(7)/(2)t^2-8t+C\\`

4.)

`s_0=5\\5=(1)/(3)(0)^3+(7)/(2)(0)^2-8(0)+C\\C=5\\s_t=(1)/(3)t^3+(7)/(2)t^2-8t+5`