Question

The velocity v of a particle moving in the xy plane is given by v = (6.0t - 4.0t2) i + 4.0 j, with v in meters per second and t (> 0) is in seconds.

What is the acceleration when t = 3.0 seconds? When is the acceleration zero? When is the velocity zero? When does the speed equal 10 m/s?

Please help :)

a= d^2/dt^2= you do it.

For the acceleration, calculate dv/dt.
dv/dt = (6.0 - 8.0 t) i
Plug in t=3 for the acceleration at that time. Set dv/dt = 0 and solve for t when acceleration = 0.
Speed is sqrt [(6t-4t^2)^2 +4^2]
Set it equal to 10 and solve for t, to do the last part of your questiuon.

so: 10=sqrt[(6t-4t^2)^2 + 4^2], so then I square both sides and get 100=[(6t-4t^2)^2 + 4^2]. Then what do I do, I'm stuck...

When is speed equal to 10m/s.

10=sqrt[(6t-4t^2)^2 +4^2]
100=[(6t-4t^2)^2 + 4^2].
subtract 4^2 from each side.
Take the square root of each side.
solve for t.

Answer 1

so when is the velocity zero then?