What is the velocity??

Question

A particle moves along the x axis according to the equation

x = 48 t + 9t2

(where t is in seconds and x is in meters). Calculate the average velocity of the particle during the first 3.0 s of its motion.

Calculate the instantaneous velocity of the particle at t = 3.0 s.

Calculate the instantaneous acceleration of the particle at t = 3.0 s.

Answer 1

Given: x=48t+9*t^2 "position"

average velocity:

Vave=change x/change time

x=48*3+9*(3)^2 = 225 meters after 3 s

Vave=225/3 = 75 m/s

x'=48+18t "velocity"

instantaneous velocity at t=3s

x'=48+54=102 m/s

Calculate the instantaneous acceleration of the particle at t = 3.0 s:

x''=18 m/s^2  "is constant"

for any time

Answer 2

To calculate velocity take the first derivative of the position function that is given,

               x(t) = 48t + 9t^2

           d/dx (x(t)) = 48 + 18t

               v(t) = 48 +18t

Calculating the average velocity for the first 3 seconds of motion:

x(t=1) = 48 + 18(1) = 66m/s

x(t=2) = 48 + 18(2) = 84m/s

x(t=3) = 48 + 18(3) = 102m/s

The average velocity then will be (66 + 84 + 102) / 3 = 84m/s

The instantaneous acceleration of the particle at 3 seconds was already calculated above: x(t=3) = 48 + 18(3) = 102m/s

Hope this helps.

Good Luck!

Answer 3

velocity is speed vs time