Question

I need help understanding the concepts involved in solving this uniform circular acceleration problem.

A train slows down as it rounds a sharp horizontal turn, going from 90.0 km/h to 50.0 km/h in the 15.0s it takes to round the bend. The radius of the curve is 150m. Compute the acceleration at the moment the train speed reaches 50.0 km/h. Assume the train continues to slow down at this time at the same rate.

Thank you so much!

Answer 1

so the total acceleration is \(\sf a=\sqrt{(a_r)^2+(a_t)^2}\)

the tangential is just the linear acceleration: \(\sf a_t=\dfrac{\Delta v}{\Delta t}\)

the radial is given by: \(\sf a_r=\dfrac{v^2}{r}\) (the velocity at 50 km/h)

Note: All these values need converted to \(\sf m/s\) first.