In the previous problem, if the particle occupies a position `x=7m` at `t=1s`, then obtain an expression for the instantaneous displacement of the particle.

Explanation

Again, we can use the idea that displacement is the integration of velocity w.r.t time.
So, `x=intvdt=int(2t+5)dt=(2t^2)/(2)+5t+c=t^2+5t+c`
where c is the constant of integration. Its value can be determined by using the given condition. (As particular details have been given about the particle.)
At `t=1s`, `x=7m=7=1^2+5xx1+cimpliesc=1m`
Hence, the expression becomes `x=t^2+5t+1`