A small frictionless cart, attached to the wall by a spring, is pulled 10 cm bac

Question

A small frictionless cart, attached to the wall by a spring, is pulled 10 cm back from its rest position and released at time t = 0 to roll back and forth for 4 sec. Its position at time t is  s=1-10cos(pi)t.                .

When is the cart moving that fast?

What is the magnitude of the acceleration then?

A small frictionless cart, attached to the wall by a spring, is pulled 10 cm back from its rest position and released at time t = 0 to roll back and forth for 4 sec. Its position at time t is s=1-10cos(pi)t. .What is the cart's maximum speed? When is the cart moving that fast? What is the magnitude of the acceleration then?

Explanation / Answer

s(t)=1-10cosPi*t.......................i)
v(t)=ds/dt= 10*Pi*sinPi*t......ii)
a(t)=dv/dt= 10*Pi^2cosPi*t=10*Pi^2*s(t).....iii)

time to max speed ; when sinPi*t=1; Pi*t=Pi/2; t=1/2 s
A)max speed = 10*Pi= 31.4 cm/s

B) time to max speed ; when sinPi*t=1; Pi*t=Pi/2 ,3Pi/2....; t=1/2 ,3/2 ,5/2 s
d)a(0.5)=10*Pi^2cosPi*1/2=0 cm/s^2

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