Question

an object starts from rest and accelerates uniformly and attains velocity of 10 metre per second for 2 seconds from there are on travels with uniform motion for another 2 second and accelerates again attaining a velocity of the next 2 second suddenly brakes applied and comes to rest after 2 seconds (A) calculate acceleration in each part of the journey (B) which part of journey is zero acceleration

Answer 1

Given:

An object starts from rest and accelerates uniformly attains a velocity of 10 $\frac{m}{s}$ for 2 seconds.

Travels  with uniform motion for another 2 seconds.

accelerates again attaining a velocity.

sudden brakes stop the object in 2 seconds.

To Find:

(A)Calculate acceleration in each part of journey

(B) Which part of journey has zero acceleration.

Solution:

1st interval of motion:

Object starts from rest u =0

Accelerates uniformly = a = constant

final velocity = 10 meter per second.

time taken = 2 seconds

Use first equation of motion

$v = u + at\\10 = 0 + a(2)\\= 5 \frac{m}{s^{2} }$

2nd interval of motion:

v = 10  $\frac{m}{s}$

uniform motion = constant velocity , therefore acceleration = 0

3rd interval of motion:

uniform acceleration for 2 seconds.

$v=u+at\\v=10+5(2)\\v=20 \frac{m}{s}$

4th interval of motion:

brakes suddenly and object stops in 2 seconds.

u = 20 v =0 a = ? t = 2    

$v = u +at\\\\0 = 20 + a(2)\\a = -10 \frac{m}{s^{2} }$

In 4th interval , object retards with retardation = 10$\frac{m}{s^{2} }$

1) acceleration in 1st part = 5$\frac{m}{s}$

2) acceleration in second part = 0

3)acceleration in 3rd part = 5$\frac{m}{s}$

acceleration in 4th part= -10$\frac{m}{s}$

B) 2nd part of journey has 0 acceleration

Answer 2

Explanation:

An object starts from rest and accelerates uniformly attains a velocity of 10 \frac{m}{s}

s

m

for 2 seconds.

Travels with uniform motion for another 2 seconds.

accelerates again attaining a velocity.

sudden brakes stop the object in 2 seconds.

To Find:

(A)Calculate acceleration in each part of journey

(B) Which part of journey has zero acceleration.

Solution:

1st interval of motion:

Object starts from rest u =0

Accelerates uniformly = a = constant

final velocity = 10 meter per second.

time taken = 2 seconds

Use first equation of motion

\begin{lgathered}v = u + at\\10 = 0 + a(2)\\= 5 \frac{m}{s^{2} }\end{lgathered}

v=u+at

10=0+a(2)

=5

s

2

m

2nd interval of motion:

v = 10 \frac{m}{s}

s

m

uniform motion = constant velocity , therefore acceleration = 0

3rd interval of motion:

uniform acceleration for 2 seconds.

\begin{lgathered}v=u+at\\v=10+5(2)\\v=20 \frac{m}{s}\end{lgathered}

v=u+at

v=10+5(2)

v=20

s

m

4th interval of motion:

brakes suddenly and object stops in 2 seconds.

u = 20 v =0 a = ? t = 2

\begin{lgathered}v = u +at\\\\0 = 20 + a(2)\\a = -10 \frac{m}{s^{2} }\end{lgathered}

v=u+at

0=20+a(2)

a=−10

s

2

m

In 4th interval , object retards with retardation = 10\frac{m}{s^{2} }

s

2

m

1) acceleration in 1st part = 5\frac{m}{s}

s

m

2) acceleration in second part = 0

3)acceleration in 3rd part = 5\frac{m}{s}

s

m

acceleration in 4th part= -10\frac{m}{s}

s

m

B) 2nd part of journey has 0 acceleration