NTA Abhyas 2020
- Exam
- NTA Abhyas
- Year
- 2020
- Subject
- Physics
- Chapter
- Motion in Two Dimensions
NTA Abhyas 2020 · Physics · Motion in Two Dimensions
The position vector of a particle is determined by the expression →...
The position vector of a particle is determined by the expression \overset{→}{r} = 2t^{2}\overset{^}{i} + 3\text{t}\overset{^}{j} + 9\overset{^}{k}. The magnitude of its displacement (in ) in first two seconds is
Correct answer
10
Step-by-step solution
\overset{\to}{r} = 2{t}^{2}\overset{^}{i} + 3t\overset{^}{j} + 9\overset{^}{k}
At t = 0, \overset{\to}{{r}_{1}} = 9\overset{^}{k}
At \text{t} = 2\text{s}, \overset{\to}{{\text{r}}_{2}} = 8\overset{^}{\text{i}} + 6\overset{^}{\text{j}} + 9\overset{^}{\text{k}}
∴ \Delta\overset{\to}{\text{r}} = \overset{\to}{{\text{r}}_{2}} - \overset{\to}{{\text{r}}_{1}} = 8\overset{^}{\text{i}} + 6\overset{^}{\text{j}}
At t = 0, \overset{\to}{{r}_{1}} = 9\overset{^}{k}
At \text{t} = 2\text{s}, \overset{\to}{{\text{r}}_{2}} = 8\overset{^}{\text{i}} + 6\overset{^}{\text{j}} + 9\overset{^}{\text{k}}
∴ \Delta\overset{\to}{\text{r}} = \overset{\to}{{\text{r}}_{2}} - \overset{\to}{{\text{r}}_{1}} = 8\overset{^}{\text{i}} + 6\overset{^}{\text{j}}