Question

Ruel is on his way to the grocery store riding his motorcycle. He started at rest in front of their house. He then travels ahead so that his distance from where he started is given by the equation:

 

  x(t)=(2.4ms2)t2−(0.120ms3)t3

 

a. Calculate the average velocity of the motorcycle for the time interval t=0 sec to t=10 sec.

b. Determine the instantaneous velocity at t=0 sec and t=5 sec

Answer 1

$x(t)=(2.4ms^{-2})t^2−(0.120ms^{-3})t^3$

(a) $x(0)=0\\x(10)=240m-120m\\V_{av}=\frac{x(10)-x(0)}{10}=\frac{240m-120m}{10s}=12ms^{-1}$

(b)$v(x)=\frac{dx}{dt}=4.8ms^{-2}t-0.36ms^{-3}t^2$

t=0, $v(x)=0$

t=5, $24ms^{-1}-9ms^{-1}=15ms^{-1}$