In a scenario where a car starts from rest and accelerates at 8 ft/sec² for 6 seconds, what is the final position of the car?

To determine the final position of a car that starts from rest and accelerates at a constant rate, we can use the equation for the position of an object under uniform acceleration. The formula is:

[ s = ut + \frac{1}{2}at^2 ]

where:

• ( s ) is the final position,
• ( u ) is the initial velocity (which is 0 since the car starts from rest),
• ( a ) is the acceleration (8 ft/sec² in this case),
• ( t ) is the time (6 seconds).

Since the car starts from rest, the initial velocity ( u ) equals 0. Plugging the values into the equation:

[ s = 0 \cdot 6 + \frac{1}{2} \cdot 8 \cdot (6^2) ] [ s = 0 + \frac{1}{2} \cdot 8 \cdot 36 ] [ s = 4 \cdot 36 ] [ s = 144 \text{ ft} ]

Thus, the final position of the car after 6 seconds of acceleration at 8 ft/sec² is indeed 144