(A) Let the position vector of a particle be $\vec{r}(t)$.$1$. The first differentiation of the position vector with respect to time $t$ gives the vel

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(A) Let the position vector of a particle be $\vec{r}(t)$.$1$. The first differentiation of the position vector with respect to time $t$ gives the velocity vector:$\vec{v} = \frac{d\vec{r}}{dt}$$2$. The second differentiation of the position vector with respect to time $t$ (or the first differentiation of velocity) gives the acceleration vector:$\vec{a} = \frac{d\vec{v}}{dt} = \frac{d^2\vec{r}}{dt^2}$Therefore,the first differentiation gives velocity and the second differentiation gives acceleration.

Class 11 Physics Motion in a Straight Line Acceleration and its graph

Easy

Which physical quantity can be found by first differentiation and second differentiation of position vector?

A
Velocity and Acceleration
B
Acceleration and Velocity
C
Displacement and Velocity
D
Speed and Distance

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Class 11 Questions

Class 11

Physics Questions

Chapter

Motion in a Straight Line

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Acceleration and its graph

What can be the angle between velocity and acceleration for the motion on a straight line? Explain with an example.

Easy

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The acceleration $(a)$ - time $(t)$ graph for a body starting from rest is given below. The maximum speed of the body is (in $m/s$)

MediumMHT CET 2025

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$A$ particle has a velocity in the negative direction and a constant acceleration in the positive direction. Match the following columns:

Column $I$ Column $II$

$(A)$ Velocity-time graph $(p)$ Slope $\rightarrow$ negative

$(B)$ Acceleration-time graph $(q)$ Slope $\rightarrow$ positive

$(C)$ Displacement-time graph $(r)$ Slope $\rightarrow$ zero

$(s)$ $|\text{Slope}| \rightarrow$ increasing

$(t)$ $|\text{Slope}| \rightarrow$ decreasing

$(u)$ $|\text{Slope}| \rightarrow$ constant

Column $I$	Column $II$
$(A)$ Velocity-time graph	$(p)$ Slope $\rightarrow$ negative
$(B)$ Acceleration-time graph	$(q)$ Slope $\rightarrow$ positive
$(C)$ Displacement-time graph	$(r)$ Slope $\rightarrow$ zero
	$(s)$ $\|\text{Slope}\| \rightarrow$ increasing
	$(t)$ $\|\text{Slope}\| \rightarrow$ decreasing
	$(u)$ $\|\text{Slope}\| \rightarrow$ constant

Medium

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The acceleration-time graph for a particle moving along the $x$-axis is shown in the figure. If the initial velocity of the particle is $-5 \, m/s$, the velocity at $t = 8 \, s$ is ....... $m/s$.

Medium

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Let $\vec v$ and $\vec a$ denote the velocity and acceleration respectively of a body in one-dimensional motion. Which of the following statements is correct regarding the speed of the body?

Medium

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Which physical quantity can be found by first differentiation and second differentiation of position vector?

Similar Questions

What can be the angle between velocity and acceleration for the motion on a straight line? Explain with an example.

The acceleration $(a)$ - time $(t)$ graph for a body starting from rest is given below. The maximum speed of the body is (in $m/s$)

The acceleration-time graph for a particle moving along the $x$-axis is shown in the figure. If the initial velocity of the particle is $-5 \, m/s$, the velocity at $t = 8 \, s$ is ....... $m/s$.

Let $\vec v$ and $\vec a$ denote the velocity and acceleration respectively of a body in one-dimensional motion. Which of the following statements is correct regarding the speed of the body?

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