A car which runs very slowly in the morning travels at a speed of $2t$ ft/s in the first $t$ seconds after it starts for $0 ≤ t ≤ 50$.

1. Draw the velocity versus time graph.

   Answer (a):

   

2. Use your graph to find the distance the car travels in the first $t$ seconds after it starts.

   Hint (b):

   

   $\text{Area}_\text{triangle}=\frac {\text{(base)(height)}}{2}$

   Answer (b):

   Distance is the area under a velocity curve.

   $\text{distance}=\frac{(t)(f(t))}{2}$

   $\text{distance}=\frac{(t)(2t)}{2} = \frac{2t^{2}}{2} = t^2$