A body with initial velocity 8.0 m/s moves along a straight line with a constant acceleration and travels 640 m in 40 seconds. For the 40 s interval find the average velocity, the final velocity and the acceleration
To find the average velocity, we use the formula:
Average velocity = (final velocity + initial velocity) / 2
We are given the initial velocity, which is 8.0 m/s. To find the final velocity, we can use the formula:
Final velocity = initial velocity + (acceleration * time)
We are given the time, which is 40 seconds. We can substitute these values into the formula to find the final velocity:
Final velocity = 8.0 m/s + (acceleration * 40 s)
To find the acceleration, we can use the formula:
Distance = initial velocity * time + (1/2) * acceleration * time^2
We are given the distance, which is 640 m, the initial velocity, which is 8.0 m/s, and the time, which is 40 seconds. We can substitute these values into the formula and solve for the acceleration.
640 m = 8.0 m/s * 40 s + (1/2) * acceleration * 40 s^2
Simplifying and rearranging the equation, we get:
640 m - 8.0 m/s * 40 s = 20 s * acceleration
640 m - 320 m = 20 s * acceleration
320 m = 20 s * acceleration
acceleration = 320 m / 20 s
acceleration = 16 m/s^2
Now that we have the acceleration, we can substitute it back into the formula to find the final velocity:
Final velocity = 8.0 m/s + (16 m/s^2 * 40 s)
Final velocity = 8.0 m/s + 640 m
Final velocity = 648 m/s
Finally, we can substitute the initial and final velocities into the formula to find the average velocity:
Average velocity = (648 m/s + 8.0 m/s) / 2
Average velocity = 656 m/s / 2
Average velocity = 328 m/s
Therefore, the average velocity is 328 m/s, the final velocity is 648 m/s, and the acceleration is 16 m/s^2.