A proton moves along the x-axis according to the equation x= 50t + 10t^2,where x

Question

A proton moves along the x-axis according to the equation x= 50t + 10t^2,where x is in meters and t is in seconds. Calculate (a) the average velocity of the proton during the first 3.0s of its motion, (b) the instantaneous velocity of the proton at t=3.0s, and (c) the instantaneous acceleration of the proton at t=3.0s. (d) Graph x versus t and
indicate how the answer to (a) can be obtained from the plot. (e) Indicate the answer to (b) on the graph. (f) Plot velocity versus time and indicate on it the answer to (c).

Explanation / Answer

(a)x=50t+10t2

At t=3, x=50(3)+10(3)2=240m

Average velocity= x/t=240/3

Vav=80 m/s.

(b) x=50t+10t2

instantaneous velocity=v= dx/dt=50+20t

at t=3

V=50+20(3)

V=110m/s

(c)a= dv/dt= d(50+20t)/dt

a=20 m/s2

(d)

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