Physics-Vectors

NEET Physics Vectors MCQ Question

Type: MCQ-numerical-Hard-Class 11

A particle moves such that its position vector is given by r(t)=(3.0t)i^+(0.2t2)j^+0.5k^\mathbf{r}(t) = (3.0t) \hat{i} + (0.2t^2) \hat{j} + 0.5 \hat{k}. What is the magnitude of its acceleration vector a(t)\mathbf{a}(t)?

A

0.4 m/s²

B

0.8 m/s²

C

2 m/s²

D

6 m/s²

Correct Answer

Option A

Detailed Explanation

The acceleration vector a(t)\mathbf{a}(t) is the second derivative of the position vector r(t)\mathbf{r}(t). Differentiating twice, we get a(t)=0i^+0.4j^+0k^\mathbf{a}(t) = 0 \hat{i} + 0.4 \hat{j} + 0 \hat{k}, with magnitude 02+0.42+02=0.4 m/s2\sqrt{0^2 + 0.4^2 + 0^2} = 0.4 \text{ m/s}^2.

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