Download App

Kinematics — Physics STD 11 — Question

Tamilnadu BoardEnglish MediumSTD 11PhysicsKinematics2 Marks
Question
Write an acceleration in terms of its component?###Show that the acceleration is the second derivative of position vector with respect to time.
✓

Answer

in terms of components, we can write,
$\vec{a}=\frac{d v_x}{d t} \hat{i}+\frac{d v_y}{d t} \hat{j}+\frac{d v_z}{d t} \hat{k}=\frac{d \vec{v}}{d t}$
$a_x=\frac{d^2 x}{d t^2}, a_y=\frac{d^2 y}{d t^2}, a_z=\frac{d^2 z}{d t^2}$
are the components of instantaneous acceleration. Since each component of velocity is the derivative of the corresponding coordinate, we can express the components $a _{ x ^{\prime}} a _{ y ^{\prime}}$ and $a _{ z }$ as $a_x=\frac{d v_x}{d t}, a_y=\frac{d v_y}{d t}, a_z=\frac{d v_z}{d t}$
Then the acceleration vector $\vec{a}$ it self is
$\vec{a}=\frac{d^2 x}{d t^2} \hat{i}+\frac{d^2 y}{d t^2} \hat{j}+\frac{d^2 z}{d t^2} \hat{k}=\frac{d^2 \vec{r}}{d t^2}$
Thus acceleration is the second derivative of position vector with respect to time.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[ 2 Marks Questions ]" from Kinematics→Kinematics — all question types→Physics STD 11 question papers→Tamilnadu Board STD 11 question papers→Tamilnadu Board question paper generator→

Similar questions

Define acceleration in SHM.
→
Lubricants are used between the two parts of a machine. Why?
→
Convert
(i) $3 m \cdot s ^{-2}$ to $km h ^{-2}$
(ii) $G =6.67 \times 10^{-11} N m ^2 kg ^{-2}$ to $cm ^3 g ^{-1} s ^{-2}$
→
What is musical scale?
→
Define work, energy, power.
→
Estimate the total number of molecules inclusive of oxygen, nitrogen, water vapour and other constituents in a room of capacity $25.0 m ^3$ at a temperature of $27^{\circ} C$ and 1 atmospheric pressure.$\left( k _{ B }=1.38 \times 10^{-23} JK ^{-1}\right)$
→
When do the real gases obey more correctly the gas equation: PV = nRT?
→
A book with printing error contains four different formulae for displacement. Choose the correct formula/formulae (a) $y=a \sin \frac{2 \pi}{ T } t$
(b) $y=a \sin v t$
(c) $y=\frac{a}{ T } \sin \left(\frac{t}{a}\right)$
(d) $y=\frac{a}{T}\left(\sin \frac{2 \pi}{ T } t+\cos \frac{2 \pi}{ T } t\right)$
→
What are stationary waves?
→
A spring of force constant K is cut into two equal pieces. Calculate force constant of each part.
→