Question

0.705
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Let a particle moving in a
Orole of radius 2m with its
speed increasing at a rate
2m/sAt an instant speed
of the particle is 2 m/s then
its net acceleration will be
22m​

Answer 1

Answer:

Explanation:

Linear speed of particle at t=2s is

v=(2)  

2

=4m/s

∴ Radial acceleration

a  

r

​  

=  

r

v  

2

 

​  

=  

2

(4)  

2

 

​  

=8m/s  

2

 

The tangential acceleration is a  

t

​  

=  

DT

DV

​  

=2t

∴ Tangential acceleration at t=2s is

a  

t

​  

=(2)(2)=4m/s  

2

 

∴ Net acceleration of particle t=2s is

a=  

(a  

r

​  

)  

2

+(a  

t

​  

)  

2

 

​  

=  

(8)  

2

+(4)  

2

 

​  

 

or a=  

80

​  

m/s  

2

 

Note: On any curved path (not necessarily a circular one) the acceleration of the particle has two components a  

t

​  

anda  

n

​  

 in two mutually perpendicular directions. Component of  

a

along  

v

 is a  

t

​  

 and perpendicular to  

v

isa  

n

​  

. Thus,

∣  

a

∣=  

a  

t

2

​  

+a  

n

2

​  

 

​