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The potential energy (in SI units) of a ...

The potential energy (in SI units) of a particle of mass `2kg` in a conservative field is `U=6x-8y`. If the initial velocity of the particle is `vecu=-1.5hati+2hatj`, then find the total distance travelled by the particle in the first two seconds.

A

`10m`

B

`12m`

C

`15m`

D

`18m`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(v)=-(delU)/(delx)hat(i)-(delU)/(dely)hat(j)=-[6hat(i)]+[8]hat(j)`
`=-6hat(i)+8hat(j)`
`:. vec(a)=-3hat(i)+4hat(j)` has same direction as that of `vec(u)=(-3hat(i)+4hat(j))/(2)=((vec(a))/(2))`
`|vec(a)|=5`
`|vec(u)|=5//2`
Since `vec(u)` and `vec(a)` are in same direction, particl will move along a straight line
`:. S=(5)/(2)xx2+(1)/(2)xx5xx2^(2)`
`=5+10=15m. 15m. Ans`
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