A particle travels for a time `2t_(0)` with velocity `v = c|t-t_(0)|`, where c is a constant. What is the distance travelled?

Explanation

The velocities at contextual times are shown in the table:

The corresponding velocity -time graph is shown in Fig 1.45

`:.` Distance travelled in time `2t_(0)`
= area enclosed by the velocity - time graph and the time -axis
= area of `Delta`AOB+area of `Delta`BCD
`= (1)/(2).t_(0).ct_(0)+(1)/(2).(2t_(0)-t_(0)).ct_(0)= (1)/(2)ct_(0)^(2)+(1)/(2)ct_(0)^(2) = ct_(0)^(2)`