Answer :
Answer:
Explanation:
a )
r = (4 + 2.5 t² )i + 5 t j
When t = 0
r₁ = 4 cm i
When t = 2s
r₂ = 14 i + 10 j
Displacement
= r₂ - r₁
=14 i + 10 j -4i
= 10i + 10j
average velocity
= displacement / time
=( 10i + 10j )/2
= 5i + 5j
b )
r = (4 + 2.5 t² )i + 5 t j
dr / dt = 5 t i + 5 j
Instantaneous velocity at t = o
(dr / dt)₀ = 5 j
Instantaneous velocity at t = 1s
(dr / dt)₁ = 5i + 5j
Instantaneous velocity at t = 2s
(dr / dt)₂ = 10i + 5 j
(a) The change in position or displacement (x) divided by the time intervals (t) in which the displacement happens is the average velocity. the magnitude and direction of the dot’s average velocity between t=0 and t=2 s will be 5 m/sec, 5 m/sec.
(b) the velocity of an object at a given point in time. . the magnitude and direction of the instantaneous velocity at t=0, t=1 s, and t=2 s. will be 10 m/sec and 5 m/sec.
(a) What is average velocity?
The change in position or displacement (x) divided by the time intervals (t) in which the displacement happens is the average velocity
given,
[tex]\vec{r}= (4+2.5t^{2})\hat{i}+5t\hat{j}[/tex]
At time t=0
[tex]r_1= 4 \hat{i}[/tex][tex]\vector{r_2} -\vector{r_1}= 14 \hat{i}+10\hat{j}-4\hat{i}[/tex]
at (t=2)
[tex]\vector{r_2}= 14 \hat{i}+10\hat{j}[/tex]
[tex]\vector{r_2} -\vector{r_1}= 10 \hat{i}+10\hat{j}[/tex]
Average velocity = [tex]\frac{\vector{r_2} -\vector{r_1}}{t_2-t_1}[/tex]
Average velocity =[tex]5\hat{i}+5 \hat{j}[/tex]
hence the magnitude and direction of the dot’s average velocity between t=0 and t=2 s will be 5 m/sec, 5 m/sec.
(b)What is instantaneous velocity?
instantaneous velocity is the velocity of an item in motion at a single point in time.
Given,
[tex]\vec{r}= (4+2.5t^{2})\hat{i}+5t\hat{j}[/tex]
[tex](\frac{ \del{r}}{\del{t}})_0= 5\hat{j}[/tex][tex](\frac{ \del{r}}{\del{t}})_2= 10\hat{i}+5\hat{j}[/tex]
[tex](\frac{ \del{r}}{\del{t}})_1= 5\hat{j}+5\hat{J}[/tex]
Hence the magnitude and direction of the instantaneous velocity at t=0, t=1 s, and t=2 s. will be 10 m/sec and 5 m/sec.
To learn more about the average velocity refer to the link ;
https://brainly.com/question/862972