During a test, automated warehouse carts P and Q travel along separate parallel lanes. At t=0t=0t=0, cart P is at position 0 m and cart Q is 0.30 m further along the aisle. The positive direction is towards the far end of the aisle.
The table gives their velocities. Between consecutive times in the table, the velocity of each cart changes uniformly.
| Time / s\mathrm{s}s | Velocity of cart P / m/s\mathrm{m/s}m/s | Velocity of cart Q / m/s\mathrm{m/s}m/s |
|---|---|---|
| 0.0 | 0.20 | 0.40 |
| 2.0 | 0.60 | 0.40 |
| 4.0 | 0.60 | 0.80 |
| 6.0 | 1.00 | 0.80 |
| 8.0 | 1.00 | 0.80 |
Calculate the displacement of cart P during the 8.0 s interval.
Calculate the displacement of cart Q during the 8.0 s interval. Compare the positions of the carts after 8.0 s and state whether cart P has caught up with cart Q.