Question

A web page designer creates an animation in which a dot on a computer screen has a position of r⃗ =[ 4.2 cm +( 2.5 cm/s2 )t2]i^+( 5.5 cm/s )tj^ .find the average velocity of the dot between t=0 and t=2.0s. give your answer as a pair of components separated by a comma. for example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. express your answer using two significant figures.

Answer 1

we are given

$r(t)=(4.2cm+(2.5cm/s^2)t^2)i+(5.5cm/s)tj$

Firstly, we will plug t=0 and t=2

Calculation of r(0):

$r(0)=(4.2cm+(2.5cm/s^2)*0^2)i+(5.5cm/s)*0j$

$r(0)=4.2i+0j$

Calculation of r(2):

$r(2)=(4.2cm+(2.5cm/s^2)*2^2)i+(5.5cm/s)*2j$

$r(2)=(4.2+5)i+(11)j$

$r(2)=(9.2)i+(11)j$

Average velocity:

now, we can use formula

$v=\frac{r(2)-r(0)}{2-0}$

now, we can plug values

$v=\frac{((9.2)i+(11)j)-(4.2i+0j)}{2-0}$

$v=\frac{5i+11j}{2-0}$

$v=(2.5cm/s) i+(5.5cm/s)j$..............Answer