The velocity of a particle which moves along the s-axis is given by v = 2-4t+5t^(3/2), where t is in seconds and v is in meters per second. Evaluate the position s, velocity v, and acceleration a when t=4s. The particle is at the position s0 =2m when t=0

a) s = 42 m

b) V = 26 m/s

c) a = 11 m/s²

Explanation:

The velocity(V) = 2 - 4t + 5t^3/2 where t is in seconds and V is in m/s

a) To get the position, we have to integrate the velocity with respect to time.

We get the position(s) from the equation:

Integrating both sides,

Integrating, we get

But at t=0, s(0) = 2 m

Therefore,

c = 2

Therefore

When t = 4,

s = 42 m

At t= 4s, the position s = 42m

b) The velocity equation is given by:

At t = 4,

V = 2 - 16 + 40 = 26 m/s

The velocity(V)at t = 4 s is 26 m/s

c) The acceleration(a) is given by:

Differentiating with respect to t,

At t = 4 s,

a = 11 m/s²