Question

3. Suppose an object increases its speed from 4.20 m/s to 5.00 m/s over 115 m. How long

does this increase in speed take?

Answer 1

By definition of average velocity,

`v_(\rm ave) = (\Delta x)/(\Delta t) = (115\,\mathrm m)/(\Delta t)`

If this object is under constant acceleration, then average velocity is also equal to the average of the initial and final velocities:

`v_(\rm ave) = \frac{v_f+v_i}2 = \frac{5.00(\rm m)/(\rm s)+4.20(\rm m)/(\rm s)}2 = 4.60(\rm m)/(\rm s)`

Then the time it takes for the object to travel 115 m with this average velocity is

`4.60(\rm m)/(\rm s) = (115\,\mathrm m)/(\Delta t) \implies \Delta t = \boxed{25\,\mathrm s}`