Question:
A body is moving with uniform acceleration. covers $200\, m$ in the first $2\, s$ and $220\, m$ in the next $4\, s$. Find the velocity in $m / s$ after $7\, s$.
A body is moving with uniform acceleration. covers $200\, m$ in the first $2\, s$ and $220\, m$ in the next $4\, s$. Find the velocity in $m / s$ after $7\, s$.
Updated On: Jun 3, 2024
- 10
- 15
- 20
- 30
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Let the initial velocity $= u$ and acceleration $= a$
In first case $s_{1}=u t_{1}+\frac{1}{2} a t_{1}^{2}$
$200=2 u +2 a \left(\therefore t_{1}=2 s \right)$
$u + a =100$ ... (i)
In second case $s_{2}=u t_{2}+\frac{1}{2} a t_{2}^{2}$
$420=6 u +18\, a \left(\therefore t_{2}=2+4=6 s\right)$
$3 a + u =70$ ... (ii)
Solving Eqs. (i) and (ii), we get
$a =-15\, ms ^{-2}$
and $u =115\, ms ^{-2}$
$v = u + at$
$=115-15 \times 7=10\, ms ^{-1}$
In first case $s_{1}=u t_{1}+\frac{1}{2} a t_{1}^{2}$
$200=2 u +2 a \left(\therefore t_{1}=2 s \right)$
$u + a =100$ ... (i)
In second case $s_{2}=u t_{2}+\frac{1}{2} a t_{2}^{2}$
$420=6 u +18\, a \left(\therefore t_{2}=2+4=6 s\right)$
$3 a + u =70$ ... (ii)
Solving Eqs. (i) and (ii), we get
$a =-15\, ms ^{-2}$
and $u =115\, ms ^{-2}$
$v = u + at$
$=115-15 \times 7=10\, ms ^{-1}$
Was this answer helpful?
0
0
Top Questions on 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
- 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
- Two cars are travelling towards each other at a speed of \( 20 \, \text{m/s} \) each. When the cars are \( 300 \, \text{m} \) apart, both the drivers apply brakes and the cars retard at the rate of \( 2 \, \text{m/s}^2 \). The distance between them when they come to rest is:
- JEE Main - 2024
- Physics
- Motion in a straight line
- A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity \(4\ ms^{-1}\). The ball strikes the water surface after \(4s\). The height of bridge above water surface is
(Take: \(g=10\ ms^{-2}\))- NEET (UG) - 2023
- Physics
- Motion in a straight line
- A bullet from a gun is fired on a rectangular wooden block with velocity u. When the bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes \(\frac{u}{3}\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:
- NEET (UG) - 2023
- Physics
- Motion in a straight line
View More Questions
Questions Asked in JKCET exam
- A moving block having mass $m$, collides with another stationary block having mass $4\,m$. The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v$, then the value of coefficient of restitution (e) will be
- JKCET - 2019
- work, energy and power
- A force $ F = 3x^2 + 2x + 1 $ acts on a body in the $ x $ -direction. The work done by this force during a displacement from $ x = -1 $ to $ +1 $ is
- JKCET - 2019
- work, energy and power
- What is the colour of the flame on heating potassium in the flame of a Bunsen burner?
- JKCET - 2019
- GROUP 1 ELEMENTS
- If $ a $ , $ b $ , $ c $ are the lengths of three edges of unit cell, $ \alpha $ is the angle between side $ b $ and $ c $ , $ \beta $ is the angle between side $ a $ and $ c $ and $ \gamma $ is the angle between side $ a $ and $ b $ , what is the Bravais Lattice dimensions of a tetragonal crystal?
- JKCET - 2019
- The solid state
- Which of the following compounds is known as copper glance?
- JKCET - 2019
- General Principles and Processes of Isolation of Elements
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.