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Alina [70]
3 years ago
6

A particle starts from rest and has an acceleration function 5 − 10t m/s2 . (a) What is the velocity function? (b) What is the p

osition function? (c) When is the velocity zero?
Physics
1 answer:
frez [133]3 years ago
7 0

Explanation:

It is given that,

A particle starts from rest and has an acceleration function as :

a(t)=(5-10t)\ m/s^2

(a) Since, a=\dfrac{dv}{dt}

v = velocity

dv=a.dt

v=\int(a.dt)

v=\int(5-10t)(dt)

v=5t-\dfrac{10t^2}{2}=5t-5t^2

(b) v=\dfrac{dx}{dt}

x = position

x=\int v.dt

x=\int (5t-5t^2)dt

x=\dfrac{5}{2}t^2-\dfrac{5}{3}t^3

(c) Velocity function is given by :

v=5t-5t^2

5t-5t^2=0

t = 1 seconds

So, at t = 1 second the velocity of the particle is zero.

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