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Motion in a Plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane3 Marks
Question
The position of a particle is given by: $\vec{\text{r}}=3.0\text{t}\hat{\text{i}}-2.0\text{t}^2\hat{\text{j}}+4\hat{\text{k}}\text{ m}$ where $t$ is in seconds, $r$ is in metres and the coefficients have the proper units.
  1. Find the velocity $v$ and acceleration $a.$
  2. What is the magnitude of velocity of the particle at $t = 2s$?
✓

Answer

$\vec{\text{r}}=3.0\text{t}\hat{\text{i}}-2.0\text{t}^2\hat{\text{j}}+4\hat{\text{k}}\text{ m}$
  1. $\vec{\text{v}}=$ velocity $=\frac{\text{d}\vec{\text{r}}}{\text{dt}}=3.0\hat{\text{i}}-4.0\text{t }\hat{\text{j }}\text{m/s}$
$\vec{\text{a}}=$ acceleration $=\frac{\text{d}\vec{\text{v}}}{\text{dt}}=-4.0\hat{\text{ j }}\text{m/s}^2$
  1. Magnitude of velocity at $t = 2s$
$\vec{\text{v}}=3.0\hat{\text{i}}-8.0\hat{\text{j}}$
$|\vec{\text{v}}|=\sqrt{(3)^2+(-8)^2}$
$=\sqrt{9+64}=\sqrt{73}\text{ m/s}$

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