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 =
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 =
= 80 m/s
b) instantaneous velocity of the proton at t = 3.0 s
Instantaneous velocity, v =

or
Instantaneous velocity, v =

= 122 m/s
c) instantaneous acceleration of the proton at t = 3.0 s
Now,
Acceleration =
= 0 + 28 = 28 m/s²