Please explain thoroughly Thanks Suppose an automobile accel

Please explain thoroughly. Thanks.

Suppose an automobile accelerates so that its velocity after t seconds is always 6t feet per second. How far does the car travel in the first 7 seconds? The distance traveled is feet.

Solution

velocit v(t)=6t

distance travelled in first 7 seconds =_{[0 to 7]}v(t) dt

distance travelled in first 7 seconds =_{[0 to 7]}6t dt

distance travelled in first 7 seconds =_{[0 to 7]}(6/2)t²

distance travelled in first 7 seconds =_{[0 to 7]}3t²

distance travelled in first 7 seconds = 3*7² -3*0²

distance travelled in first 7 seconds = 147 feet