45. A particle moves in a straight line with an initial velocity of 30 m/s and constant acceleration 30 m/s2 . (a) What is its displacement at t = 5 s? (b) What is its velocity at this same time?

Applying the fundamental theorem of the calculation dx/dt = 5t + vo. The speed equation is V (t) = 5t + vo. Since the initial velocity is 30m/s, V (0) = 5 (0) + vo = 30. Therefore, V (t) = dx/dt = 5t + 30. Applying again the fundamental theorem of the calculation X (t) = 5t^2 / 2 + 30t + xo.

Displacement in 5 seconds is given by X (5) - X (0).

X (5) - X (0) = 5 (5)^2/2 +3 (5) + Xo - 5 (0)^2/2 -3 (0) -Xo = 155/2

Displacement after 5 seconds is 155/2 meters

david8644 david8644 · Answer 2 · 2019-12-16T21:55:22+01:00

Answer:

Velocity at 5 seconds: 180 m/s

Ditance: 525 meters

Explanation:

In order to calculate displacement in this option we need to use the formula for distance when an object is experimenting aceleration:

[tex]s=VoT+1/2at^2[/tex]

So now we just have to insert the data that we know:

[tex]s=VoT+1/2at^2\\s= 30*5+ 1/2*30*25\\s=150+15*25\\s= 150+375\\s=525 m[/tex]

The distance after 5 seconds with an initial velocity of 30 m/s and an acceleration of 30 m/s will be 525 meters.

And the final velocity is calculated by the next formula:

[tex]Vf= Vo+ A*t\\Vf= 30 m/s+ 30m/s*5\\Vf=180m/s[/tex]

So the final velocity at 5s would be 180 m/s