Final answer:
To determine the distance an object with an initial velocity of 5 m/s moving with an acceleration of 3 m/s² for 8 seconds travels, we use the kinematic equation \( s = ut + \frac{1}{2}at^2 \). The calculation shows that the object travels a total of 136 meters.
Step-by-step explanation:
To calculate how far an object moves in a certain time period while experiencing acceleration, we can use the kinematic equation for uniformly accelerated motion, which is:
\( s = ut + \frac{1}{2}at^2 \)
where:
- s is the displacement
- u is the initial velocity
- a is the acceleration
- t is the time
In this case, the object's initial velocity (u) is 5 m/s, the acceleration (a) is 3 m/s², and the time (t) is 8 seconds. Plugging these values into the equation gives us:
\( s = 5 m/s \times 8 s + \frac{1}{2} \times 3 m/s² \times (8 s)^2 \)
\( s = 40 m + \frac{1}{2} \times 3 \times 64 \)
\( s = 40 m + 96 m \)
\( s = 136 m \)
The object moved 136 meters in that time.