How Do You Solve for Time in the Kinematics Equation s = ut + 1/2 at^2?

[kitehigh]

i need to make a model for predicting the time taken for a ball to roll a certain distance up a ramp, i can't work out how to get time in terms of initial velocity, acceleration (const.) and displacement.

how do i make t the subject in

s = ut + 1/2 at^2

or ios there another equation i can use?

 

[topsquark]

i need to make a model for predicting the time taken for a ball to roll a certain distance up a ramp, i can't work out how to get time in terms of initial velocity, acceleration (const.) and displacement.

how do i make t the subject in

s = ut + 1/2 at^2

or ios there another equation i can use?

That looks like it ought to work. Make sure you pick a direction for +s...i.e. the acceleration and the initial velocity will be in opposite directions. Also, if you don't know already, the acceleration will depend on the angle the board is at: a = gcos(theta). With that, use the quadratic formula to solve your equation for t. One of your solutions will be the one you want, one will be much longer representing the time it takes for the ball to roll up the ramp to its maximum and roll back down to s.

-Dan