Question:
A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the $4^{th}$ second compared to that in the $3^{rd}$ second is
A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the $4^{th}$ second compared to that in the $3^{rd}$ second is
Updated On: Apr 19, 2024
- $33\%$
- $40\%$
- $66\%$
- $77\%$
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
We know that
$S_{n t h}=u+\frac{1}{2} a(2 n-1) $
$S_{3 \text { rd }}=0+\frac{1}{2} a(2 \times 3-1)=\frac{5}{2} a ($ for $ n=3 s)$
$S_{4 t h}=0+\frac{1}{2} a(2 \times 4-1)=\frac{7}{2} a ($ for $n=4 s )$
So, the percentage increase
$=\frac{S_{4 h }-S_{3 rd }}{S_{3 rd }} \times 100$
$=\frac{\frac{7}{2} a-\frac{5}{2} a}{\frac{5}{2} a} \times 100$
$=\frac{\frac{2 a}{2}}{\frac{5}{2} a} \times 100$
$=2 \times 20=40 \%$
$S_{n t h}=u+\frac{1}{2} a(2 n-1) $
$S_{3 \text { rd }}=0+\frac{1}{2} a(2 \times 3-1)=\frac{5}{2} a ($ for $ n=3 s)$
$S_{4 t h}=0+\frac{1}{2} a(2 \times 4-1)=\frac{7}{2} a ($ for $n=4 s )$
So, the percentage increase
$=\frac{S_{4 h }-S_{3 rd }}{S_{3 rd }} \times 100$
$=\frac{\frac{7}{2} a-\frac{5}{2} a}{\frac{5}{2} a} \times 100$
$=\frac{\frac{2 a}{2}}{\frac{5}{2} a} \times 100$
$=2 \times 20=40 \%$
Was this answer helpful?
0
0
Top Questions on Motion in a straight line
- The displacement and the increase in the velocity of a moving particle in the time interval of \( t \) to \( (t + 1) \) s are 125 m and 50 m/s, respectively. The distance travelled by the particle in \( (t + 2)^{\text{th}} \) s is \( \_\_\_\_ \) m.
- JEE Main - 2024
- Physics
- Motion in a straight line
- A bus moving along a straight highway with speed of 72 km/h is brought to halt within 4s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _______m.
- JEE Main - 2024
- Physics
- Motion in a straight line
- Pebbles are dropped freely for every half second into a river from a bridge above it. When the first pebble is about to strike the surface of the water, the fifth pebble is dropped. Then the height from the surface of the water from which the pebbles are dropped is (Acceleration due to gravity = 10 m/s²).
- TS EAMCET - 2024
- Physics
- Motion in a straight line
- A long straight wire carrying a current 3 A produces a magnetic field \( B \) at a certain distance. The current that flows through the same wire will produce a magnetic field \( \frac{B}{3} \) at the same distance is:
- KEAM - 2024
- Physics
- Motion in a straight line
- The motion of a cylinder on an inclined plane is:
- KEAM - 2024
- Physics
- Motion in a straight line
View More Questions
Questions Asked in WBJEE exam
- In the following sequence of reactions, compound 'M' is:
\( \text{M} \xrightarrow{\text{CH}_3\text{MgBr}} \text{N} + \text{CH}_4 \uparrow \xrightarrow{\text{H}^+} \text{CH}_3\text{COCH}_2\text{COCH}_3 \)
- WBJEE - 2024
- Organic Chemistry
Identify the ion having 4f\(^6\) electronic configuration.
- WBJEE - 2024
- Some Applications of d- and f-Block Elements
- Metallic conductors and semiconductors are heated separately. What are the changes in conductivity?
- WBJEE - 2024
- Conductivity-thermal and electrical
- The equivalent weight of \(\text{Na}_2\text{S}_2\text{O}_3\) (Gram molecular weight = \(M\)) in the given reaction is:
\[\text{I}_2 + 2 \text{Na}_2\text{S}_2\text{O}_3 \rightarrow 2 \text{NaI} + \text{Na}_2\text{S}_4\text{O}_6\]- WBJEE - 2024
- Redox reactions
- The reactivity order of the following molecules towards SN1 reaction is:
Allyl chloride (I), Chlorobenzene (II), Ethyl chloride (III)- WBJEE - 2024
- Reaction mechanisms
View More Questions
Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.