Question

FIGURE EX2.8 shows the velocity graph for a particle having

initial position $x_o=0m$at $t_o=0s$. At what time or times is the particle found at$x=35m$?

Short answer

The particle will be found at $x=35m$in two times$6s$and$10s.$

Step-by-step solution

Given information

A speed-time curve is given in this question. So the area under the curve determines the position of the particle within a certain interval of time.

Determination of time

The particle starts moving from $\left(x_i=0,t=0\right)$.

Now, each of the square grid in the graph has a length of ,

$l=\left(5m/s\right)\left(2s\right)=10m$.

To cover $x=35m$, the particle has to move up to $3.5$squares under the curve, as role="math" localid="1648750976474" $\left(3.5\times 10m=35m\right)$.

So considering time coordinate, $3.5$number of squares are completed at $t=6s.$

If we consider the half portion of the square that cancels out between $6s$and $8s$, then to cover the same distance, the particle needs to move up to $t=10s.$

Hence the particle will be found at$x=35m$at times$6s$and$10s.$