Question

A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by𝑥(𝑡)=𝑏𝑡2−𝑐𝑡3,𝑤ℎ𝑒𝑟𝑒𝑏=2.4𝑚𝑠−1𝑎𝑛𝑑𝑐=0.120𝑚𝑠−3(a)Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s.(b)Calculate the instantaneous velocity of the car at t =0, t = 5.0 s and t = 10.0 s.

Answer 1

$x (t) = bt^2-ct^3$

$a)$

$v_{avg}= \frac{x(t_2)-x(t_1)}{t_2-t_1};$

$x(0) = 0$

$x(10)= 2.4*10^2-0.12*10^3= 240-120 = 120$

$v_{avg}= \frac{x(10)-x(0)}{10- 0}= 12\frac{ m}{ s}$

$b)$

$v(t)= x'(t) = (bt^2-ct^3)'=2bt-3ct^2$

$v(0) =0$

$v(5)= 2*2.4*5-3*0.12*25=15\frac{ m}{ s}$

$v(10)=2*2.4*10-3*0.12*100=12\frac{ m}{ s}$

$\text{Answer :}a)v_{avg}= 12\frac{ m}{ s}$

$\text{ } b)v(0) =0;v(5)=15\frac{ m}{ s};v(10)=12\frac{ m}{ s}$