The displacement of a particle is given by x = (t - 2)2 where x is in meters and t in seconds. The. distance covered by the particle in the first 4 seconds is

1. 4 m
2. 8 m
3. 12 m
4. 16 m

(b) Hint: Area of v-t graph without signs gives the distance.

Step 1: Find the velocity and acceleration of the particle.

 Given, x=(t2)2 Velocity, v=dxdt=ddt(t2)2=2(t2)m/s Acceleration, a=dvdt=ddt[2(t2)]=2[10]=2m/s2 When, t=0;v=4m/st=2s;v=0m/st=4s;v=4m/s

Step 2: Draw v-t graph.

v - t graph is shown in the adjacent diagram.

Step 3: Find the distance covered by the particle.
Distance traveled = area of the graph

= areaOAC+ area ABD= 4×22+12×2×4=8m