Question

the position vector of a particle is determined by the expression vector R equals to 3 t raised to 2 I CAP + 4 t raised to 2 J cap + 7 k cap the distance travelled in first 10 seconds is​

Answer 1

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Maybe U asked Displacement. Calculating distance will be cumbersome as it is some complex parabola

r (i)= Initial position vector

r (f) = Final position vector

Since r is the finction of time.

r(i)=r(0)=7 k^   

r(f)=r(10)=3*10² i^ + 4*(10)² j^ +7 k^

Now ,

Displacement vector= r(f)-r(i)

D= |300 i^ + 400j^ +(7-7)k^ |

 

=500 

(a) is correct !!

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Answer 2

Explanation:

according to question R is function of time so so it will change according to to time initial and final

therefore to find displacement or distance for first 10 seconds initially we must start from zero second then final position will be at 10 second

substituting the values in the equation we get position of the vector

now subtract final position from initial position you will get your displacement

hope it is helpful for you