Solving a Particle Displacement Problem: Find the Speed at x=2.5

[thereddevils]

Homework Statement

A particle moves along the positivex-axis .At time t seconds after leaving a fixed point O from rest, the displacement of the particle from O is x cm. The acceleration, a of the particle is defined by

a=5-3t , 0<=t<=1

=-(4t+1), t>1

Find the speed of the particle when x=2.5

Homework Equations

The Attempt at a Solution

Integrate twice to get the displacement function,

x=5t^2/2-t^3/2 , 0<=t<=1

= -2/3t^3-2t^2 ,t>1

so 5t^2/2-t^3/2=2.5

solving this does not give me the answer. Where have i gone wrong?

 

[Swap]

ur mistake is u considered only one condition thus u integrated only for 0<=t<=1. How r u sure u that at the time the particle will be at x=2.5 will be less than or equal to 1s. In fact if u do some calculation u will find its not true. thus u have to apply the second condition for t.

 

[thereddevils]

ur mistake is u considered only one condition thus u integrated only for 0<=t<=1. How r u sure u that at the time the particle will be at x=2.5 will be less than or equal to 1s. In fact if u do some calculation u will find its not true. thus u have to apply the second condition for t.

But even when i considered the other one, i don get the answer too which is 1.5m

 

[Swap]

actually u have to apply both integrating part by part.

 

[thereddevils]

actually u have to apply both integrating part by part.

sorry but i don get what u mean

 

[thereddevils]

any other insights to this problem?

 

[hikaru1221]

The way I see your work, in the 2nd integration to find x of t>1s, you set the lower limits as x=0 and t=0, right? Have it checked. That's wrong. Remember that you are considering t>1s; t=0 doesn't fit.