Question

Velocity-time graph of a particle moving in a straight line is shown in figure. At time t=0, s=20 m. Plot a-t and s-t graphs of the particle.

Answer 1

for acceleration vs time graph:

$fromt=0tot=4;a=0m{s}^{-2}$

from $t=4tot=6changeinvelocity=20m/s;a=10m{s}^{-2}$

from $t=6tot=8$ change in velocity$=-20m/s;a=-10m{s}^{-2}$

from $t=8tot=12$ change in velocity$=40m/s;a=10m{s}^{-2}$

from $t=12tot=14$ change in velocity$=20m/s;a=-10m{s}^{-2}$

for displacement vs time graph:

change in displacement is an area under the v vs t graph

so

from t=0 to t=4

as velocity is constant so the graph of s vs t will be linear

change in diplacement=-80m

from t=4 to t=6

as velocity is linearly changing the s vs t will vary parabolically

change in diplacement=-20m

from t=6 to t=8

as velocity is linearly changing the s vs t will vary parabolically

change in displacement=-20m

from t=8 to 12

as velocity is linearly changing the s vs t will vary parabolically

change in displacement =0m

from t=12 to t=14

as velocity is linearly changing the s vs t will vary parabolically

change in diplacement=20m