Question

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

Answer 1

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.