# Thread: differentiation - velocity and acceleration

1. ## differentiation - velocity and acceleration

Hello everyone,

I am currently stuck on the following question for exam revision and need help, could someone please go step by step so I understand this.

The displacement ’y’ mm of a slide value of an engine is given by the expression

y = t2 ln 4t
3sint

a) Find the expression for velocity of the valve
b) Evaluate the velocity in ms-1 when t =20 x 10-3 seconds

Thank you Phill

2. Originally Posted by Anamcaraash
Hello everyone,

I am currently stuck on the following question for exam revision and need help, could someone please go step by step so I understand this.

The displacement ’y’ mm of a slide value of an engine is given by the expression

y = t2 ln 4t
3sint

a) Find the expression for velocity of the valve
b) Evaluate the velocity in ms-1 when t =20 x 10-3 seconds

Thank you Phill
Do you mean $y= \frac{t^2 ln(4t)}{3 sin t}$. That's a bit tedious but nothing terribly difficult. Use the "quotient", "product" and "chain rules" (the last just to differentiate ln(4t)). What have you tried and where did you go wrong?