35.7k views
0 votes
A proton moves along the x axis according to the equation x = 38 t + 14 t2, 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.

User Nij
by
7.0k points

1 Answer

2 votes

Answer:

a) 240 m

b) 122 m/s

c) 28 m/s²

Step-by-step explanation:

Given:

Equation for motion

x = 38t + 14t²

a) average velocity during first 3 seconds

average velocity =
\frac{\textup{change in displacement}}{\textup{cahnge in time}}

now,

distance, at t = 0 s

x = 38 × 0 + 14 × 0² = 0 m

distance, at t = 3 s

x = 38 × 3 + 14 × 3² = 240 m

therefore,

average velocity =
(240-0)/(3-0) = 80 m/s

b) instantaneous velocity of the proton at t = 3.0 s

Instantaneous velocity, v =
(dx)/(dt)=38+28* t

or

Instantaneous velocity, v =
(dx)/(dt)=38+28* 3

= 122 m/s

c) instantaneous acceleration of the proton at t = 3.0 s

Now,

Acceleration =
(dv)/(dt) = 0 + 28 = 28 m/s²

User Nikopol
by
6.3k points