Question

A proton moves along the x axis according to the equation x = 62 t + 14 t^2, where x is in meters and t is in seconds. Calculate (a) the average velocity of the proton during the first 3.0 s of its motion, (b) the instantaneous velocity of the proton at t = 3.0 s, and (c) the instantaneous acceleration of the proton at t = 3.0 s.

Answer 1

Answer on Question #51383, Physics - Mechanics - Kinematics - Dynamics

Question A proton moves along the x axis according to the equation $x=62t+14t^{2}$, where x is in meters and t is in seconds. Calculate (a) the average velocity of the proton during the first 3.0 s of its motion, (b) the instantaneous velocity of the proton at t = 3.0 s, and (c) the instantaneous acceleration of the proton at t = 3.0 s.

Solution (a) Average velocity is total displacement divided by total time.

$\bar{v}=\frac{s}{t}=\frac{x=62\cdot 3+14\cdot 3^{2}}{3}=104\,m/s$

(b)instantaneous velocity is

$v(t)=x^{\prime}(t)=62+28\cdot t$

At t=3.0 :

$v(3)=62+28\cdot 3=146\,m/s$

(c)instantaneous acceleration is

$a(t)=v^{\prime}(t)=28$

At t=3.0 :

$a(3)=28\,m/s^{2}$

http://www.AssignmentExpert.com/