From the veloicty time graph of a particle given in figure describe the motion of the particle qualitively int eh interval 0 to 4s. Find a. the distance travelled during first two seconds, b. during the time 2s to 4s, c. during the time 0 to 4s d. displacement during 0 to 4 s. e. acceleration at t=1/2 and f. acceleration at t=2s
.

Options

A. `20 m` `20 m`
B. `20 m` `30 m`
C. `30 m` `20 m`
D. `10 m` `20 m`

Answer

D

Explanation

At t=0, the particle is at rest say at the origin. After that the velocity is positive, so that the particle moves in the positive x direction. Its speed increases till 1 second when it starts decreasing. The particle continues to move further in positive x direction. At t=2s, its velocity is reduced to zero, it has moved through a maximum positive x distance. Then it changes its direction, velocity being negative, but increasig i magnitude.At t=3s velocity is maximum in the negative x direction and then the magnitude starts decreasing. it comes to rest at t=4 s.
a. Distance during 0 to 2 s = Area of OAB
`=1/2xx2sxx10 m/s=10m`
b. Distance during 2 to 4s = Area of BCD = 10 m. The partile has mioved in negative x direction during this period.
c. The distance travelled during 0 to 4s=10 m+10m
`=20 m`
d. displacement during 0 to 4 = 10 m+(-10m)=0
e. at t=1/2 s acceleration = slope of line OA=10 m/s^2
f. at t=2 s acceleration= slope of line ABC = - 10 m/s^2.