Question

A particle is moving along a straight line through a fluid medium such that its speed is measured as v=(2t) m/s, where t is in seconds. If it is released from rest at s=0, determine its positions and acceleration when t=3 s.

Answer 1

2 m/s², 19.62 m

Step-by-step explanation:

v = Final velocity = 2t

t = Time taken

u = Initial velocity

s = Displacement

a = Acceleration

From the equation of motion

`v=u+at\\\Rightarrow a=(v-u)/(t)\\\Rightarrow a=(2t-0)/(t)\\\Rightarrow a=2\ m/s^2`

The acceleration of the particle is 2 m/s²

at t = 3 seconds

`s=ut+(1)/(2)at^2\\\Rightarrow s=0* t+(1)/(2)* 2* 3^2\\\Rightarrow s=19.62\ m`

The position at t = 3 seconds is 19.62 m