Calculus Problems

Question

A particle moves on the x-axis so that its position at time t is S(t) = (t² - t)/ (t-1). at what values(s) of t the velocity is Zero? 

Answer 1

The original function has a domain restriction; t ≠ 1

 

S'(t) represents the velocity at time t.

 

S'(t) = [(t - 1)(2t - 1) - (t² - t)(1)]/[(t - 1)²]

 

Even more straight forward, the original simplifies to S(t) = t(t - 1)/(t - 1) = t

 

S'(t) = 1

 

The velocity of the particle is constant at t, t ≠ 1, and v = 1, v ≠ 0 and v is undefined at t = 1.

 

A²

 

 

 

 

Answer 2

Hi Mah,

Remember that dx/dt gives the instantaneous velocity of the particle. Also, you may want to simplify s(t) (which is x(t) ) before applying calculus. 

Hope this helps

Ryan