Question

a particle moves on x axis as per equation x= t^3-9t^2+15t+2 . Distance travelled by particle between t=0 and t=5s is​

Answer 1

Explanation:

Here in the given equation just replace the ' t' s with the given time .

First of all put 0 in place of t

which will give you 2

which implies when time was 0 body was already in position 2m from the origin .....

Now as it's asked to calculate the distance upto 5 seconds....put 5 in place of t

which will give : 37m

so the distance travelled:

(37-2) : 35m

Answer 2

The distance travelled by particle between t = 0 and t = 5 s is​ 25 m

Given: a particle moves on x-axis as per equation x = t³ - 9 t² + 15 t + 2.

To Find: Distance travelled by particle between t=0 and t=5s

Solution:

• We can find the distance travelled by the particle by the formula,

               Distance = Distance ( at t = 5 s ) - Distance ( at t = 0 )       .....(1)

• Distance ( at t = 5 s ) can be found by substituting t = 5 s in the equation of x.
• Distance ( at t = 0 s ) can be found by substituting t = 0 s in the equation of x.

        x = t³ - 9 t² + 15 t + 2

    Distance ( at t = 5 s ) = ( 5 )³ - 9 ( 5 )² + 15 × 5 + 2

                                       = - 23 m

    [ negative sign means the particle is moving in the opposite direction ]

     Distance ( at t = 0 s ) = ( 0 )³ - 9 ( 0 )² + 15 × 0 + 2

                                       =  2 m

From (1), we get;

       Distance = Distance ( at t = 5 s ) - Distance ( at t = 0 )

                       = ( - 23 - 2 ) m

                       = - 25 m

 [ negative sign means the particle is moving in the opposite direction

Hence, the distance travelled by particle between t = 0 and t = 5 s is​ 25 m.

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