Question

A particle moves along the x-axis so that at time t≥0 its position is given by x(t)=2t3−9t2−60t+4. What is the total distance traveled by the particle over the time interval 0≤t≤7 ?

Answer 1

Answer: 175

Step-by-step explanation:

Hi, to answer this question we have to substitute x=0 and x=7 in the equation:

t=0

x(0)=2(0)3−9(0)2−60(0)+4 =4

t=7

x(7)=2(7)3−9(7)2−60(7)+4 =2(343)-9(49)-420+4

= 686-441-420+4= -171

So, to obtain the distance traveled we have to subtract:

t(7)-t(0)= -171-(4) = -175 = ║175║(absolute value)=175

Feel free to ask for more if needed or if you did not understand something.

Answer 2

Answer:

-175 or 175  along the x-axis in a negative direction

Step-by-step explanation:

The distance is the total length of the trajectory made by a moving object between two points. We need to find the total distance traveled by a particle over the time interval  $t\in[0,7]$ , so:

Let:

$d_o=Distance\hspace{3}traveled\hspace{3}at\hspace{3}t=0\\d_f=Distance\hspace{3}traveled\hspace{3}at\hspace{3}t=7$

Using the equation provided by the problem:

$x(t)=2t^3-9t^2-60t+4$

For t=0

$x(0)=2*(0)^3-9*(0)^2-60*(0)+4=0-0-0+4=4$

For t=7

$x(7)=2*(7)^3-9*(7)^2-60*(7)+4=686-441-420+4=-171$

Hence, the total distance traveled by the particle over the time interval 0≤t≤7 is:

$Total\hspace{3}distance\hspace{3}traveled=d_t=d_f-d_o=-171-4=-175$