A new electric car is capable of accelerating from $0{\text{ms}}^{-1}$ to $27{\text{ms}}^{-1}$ in $2.4\text{s}.$

Given below is a sample of its velocities, $v(t)$ meters per second, at time $t$ seconds during its path.

1. By forming a Riemann sum of expressions of the form

   $$v(t_{i-1})\mathrm{\Delta }t$$

   find an estimate for the total distance traveled by the car.

2. Explain the meaning of the expression

   $${\int }_0^{2.4}v(t)dt$$

Give your answer to part (a)