The acceleration of the particle at t = 1 s is, The position of a particle is given by where is in seconds and the coefficients have the proper units for to be in metres

Question

The position of a particle is given by $\vec{r} = 3 t \hat{i} + 2 t^{2} \hat{j} + 5 \hat{k},$ where $t$ is in seconds and the coefficients have the proper units for $\vec{r}$ to be in metres. The acceleration of the particle at t = 1 s is

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(3)

$Given : \vec{r} = 3 t \hat{i} + 2 t^{2} \hat{j} + 5 \hat{k}$

$\vec{r}$

$\vec{v} = 3 \hat{i} + 4 t \hat{j} {m s}^{- 1}$

$∴$ $Acceleration, \vec{a} = \frac{d \vec{v}}{d t} = 4 \hat{j} {m s}^{- 2}$

$Acceleration of the particle remains constant all the time.$

Solution

Q.
The position of a particle is given by $\vec{r} = 3 t \hat{i} + 2 t^{2} \hat{j} + 5 \hat{k},$ where $t$ is in seconds and the coefficients have the proper units for $\vec{r}$ to be in metres. The acceleration of the particle at t = 1 s is

1 $2 \hat{j} {m s}^{- 2}$

2 $- 2 \hat{j} {m s}^{- 2}$

3 $4 \hat{j} {m s}^{- 2}$

4 $- 4 \hat{j} {m s}^{- 2}$

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Solution

Q. The position of a particle is given by r→=3ti^+2t2j^+5k^, where t is in seconds and the coefficients have the proper units for r→ to be in metres. The acceleration of the particle at t = 1 s is

1 2j^ m s-2

2 -2j^ m s-2

3 4j^ m s-2

4 -4j^ m s-2