CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

1st Equation of Motion

Starting from...

Question

Starting from rest a particle is first accelerated for time $t_{1}$ with constant acceleration $a_{1}$ and then stops in time $t_{2}$ with constant retardation $a_{2} .$ Let $v_{1}$ be the average velocity in this case and $s_{1}$ the total displacement. In the second case
it is accelerated for the same time $t_{1}$ with constant acceleration $2 a_{1}$ and come to rest with constant retardation $a_{2}$ in time $t_{3} .$ If $v_{2}$ is the average velocity in this case and $s_{2}$ the total displacement, then

A

v_{2} = 2 v_{1}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

2 v_{1} < v_{2} < 4 v_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

S_{2} 2 = S_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

2 S_{1} < S_{2} < 4 S_{1}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct options are
A $v_{2} = 2 v_{1}$
D $2 S_{1} < S_{2} < 4 S_{1}$
Velocity after acceleration by $a$ for $t_{1}$ time= $a_{1} t_{1}$
It takes time $t_{2}$ to retard to zero velocity, so, $a_{1} t_{1} = a_{2} t_{2}$
$⟹ t_{2} = \frac{a_{1}}{a_{2}} t_{1}$
Similarly for second case,
$t_{3} = \frac{2 a_{1}}{a_{2}} t_{1}$
In first case,
Distance traveled during acceleration= $\frac{1}{2} a_{1} t_{1}^{2}$
Distance traveled during retardation= $\frac{(a_{1} t_{1})^{2}}{2 a_{2}}$
$⟹ s_{1} = \frac{1}{2} a_{1} t_{1}^{2} + \frac{a_{1}^{2} t_{1}^{2}}{2 a_{2}}$
$v_{1} = \frac{s_{1}}{t_{1} + t_{2}} = \frac{s_{1}}{t_{1} + \frac{a_{1}}{a_{2}} t_{1}} = \frac{1}{2} a_{1} t_{1}$
In second case,
Distance traveled during acceleration= $a_{1} t_{1}^{2}$
Distance traveled during retardation= $\frac{(2 a_{1} t_{1})^{2}}{2 a_{2}}$
$⟹ s_{2} = a_{1} t_{1}^{2} + \frac{2 a_{1}^{2} t_{1}^{2}}{a_{2}}$
$v_{2} = \frac{s^{2}}{t_{1} + t_{3}} = \frac{s_{2}}{t_{1} + \frac{2 a_{1}}{a_{2}} t_{1}} = a_{1} t_{1}$
Hence $v_{2} = 2 v_{1}$
And $2 s_{1} < s_{2} < 4 s_{1}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Starting form rest a particle is first accelerated for time

t_{1}

with constant acceleration

a_{1}

and then stops in time

t_{2}

with constant retardation

a_{2}

v_{1}

be the average velocity in this case and

s_{1}

be the total displacement. In the second case, it is accelerated for the same time

t_{1}

with constant acceleration

2 a_{1}

and comes to rest with constant retardation

a_{2}

t_{3}

v_{2}

is the average velocity in this case and

s_{2}

the total displacement. Then

Q. A particle moves with constant acceleration. If v1, v2 and v3 are the three average velocities in three successive intervals t1, t2 and t3 of time. Then prove that v1-v2/v2- v3 = t1 + t2/t2+ t3

Q. A point moves with uniform acceleration and

v_{1}, v_{2}, v_{3}

denote the average velocities in three successive intervals of time

t_{1}, t_{2}, t_{3}

. Then, the relation

\frac{v_{1} - v_{2}}{v_{2} - v_{3}}

Q. A train accelerates from rest at a constant rate

a_{1}

S_{1}

t_{1}

. After that it retards to rest at a constant rate

a_{2}

S_{2}

t_{2}

. Then the correct relation among the following is

A particle moves with velocity $v_{1}$ for time $t_{1}$ and $v_{2}$ for time $t_{2}$ along a straight line. The magnitude of the average acceleration is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Motion Under Constant Acceleration

PHYSICS

Watch in App

explore_more_icon

Explore more

1st Equation of Motion

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon