1
NEET 2024 (Re-Examination)
+4
-1

A particle is moving along $$x$$-axis with its position (x) varying with time $$(t)$$ as $$x=\alpha t^4+\beta t^2+\gamma t+\delta$$. The ratio of its initial velocity to its initial acceleration, respectively, is:

A
$$2 \alpha: \delta$$
B
$$\gamma: 2 \delta$$
C
$$4 \alpha: \beta$$
D
$$\gamma: 2 \beta$$
2
NEET 2024
+4
-1

The velocity $$(v)-$$ time $$(t)$$ plot of the motion of a body is shown below:

The acceleration $$(a)-$$ time $$(t)$$ graph that best suits this motion is :

A
B
C
D
3
NEET 2023 Manipur
+4
-1

The position of a particle is given by

$$\vec{r}(t)=4 t \hat{i}+2 t^2 \hat{j}+5 \hat{k}$$

where $$\mathrm{t}$$ is in seconds and $$\mathrm{r}$$ in metre. Find the magnitude and direction of velocity $$v(t)$$, at $$t=1 \mathrm{~s}$$, with respect to $$\mathrm{x}$$-axis

A
$$4 \sqrt{2} \mathrm{~ms}^{-1}, 45^{\circ}$$
B
$$4 \sqrt{2} \mathrm{~ms}^{-1}, 60^{\circ}$$
C
$$3 \sqrt{2} \mathrm{~ms}^{-1}, 30^{\circ}$$
D
$$3 \sqrt{2} \mathrm{~ms}^{-1}, 45^{\circ}$$
4
NEET 2023
+4
-1

A vehicle travels half the distance with speed $$v$$ and the remaining distance with speed $$2 v$$. Its average speed is :

A
$$\frac{2 v}{3}$$
B
$$\frac{4 v}{3}$$
C
$$\frac{3 v}{4}$$
D
$$\frac{v}{3}$$
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