Answer to Question #175019 in Classical Mechanics for Mary Chumanni

Question

A car stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by xt=bt2-ct3 where, b=2.40m/s2 and c=0.120m/s3

A.) Calculate the average velocity of the car for the time interval t=0s to t=10.0s

B.) Calculate the instantaneous velocity of the car at t=0s; t=5.0s; and t=10.0s

Answer 1

Answer

A. distance from the light is given by $x(t) =bt^2-ct^3$

where, b=$2.40m/s^2$ and c=$0.120m/s^3$

distance from the light is given by

$x(t) =bt^2-ct^3$ at t=0

x=0 m

At t=10sec

$x(t) =2.40\times 100-0.12\times1000$

=120m

the average velocity of the car for the time interval t=0s to t=10.0s

$V_a=\frac{dx}{dt}\\=\frac{120-0}{10-0}\\=12m/s$

B. the instantaneous velocity of the car at t=0s; t=5.0s; and t=10.0s

$v=\frac{dx}{dt}=2bt-3ct^2$

So at t=0 v=0

At t=5sec

$v=2\times2.4\times5-3\times0.12\times25\\=15m/s$

At t=10

$v=2\times2.4\times10-3\times0.12\times100\\=12m/s$