Question

The acceleration of a particle is increasing linearly
with time t as bt. The particle starts from origin
with an initial velocity vo. The distance travelled by
the particle in time t will be
​

Answer 1

Answer:

here it is given that a=bt

wkt, a=  

change in time

change in velocity

​  

=  

dt

dv

​  

 

∴  

dt

dv

​  

=bt now integrating this we will get v

v=  

2

bt  

2

 

​  

+c

At t=0 s, v=v  

0

​  

, Thus v  

0

​  

=c

∴v=  

2

bt  

2

 

​  

+v  

0

​  

 

Now. v=  

change in time

change in position

​  

=  

dt

ds

​  

=  

2

bt  

2

 

​  

+v  

0

​  

 

∴ds=(  

2

bt  

2

 

​  

+v  

0

​  

)dt

∴ Integrating the above we get, s=  

6

bt  

3

 

​  

+v  

0

​  

t+c  

′

 

at t=0, s=0∴c  

′

=0

i.e. s=  

6

bt  

3

 

​  

+v  

0

​  

t

Explanation: