I'm struggling to figure out velocity and understanding the formulas. My question I have to try and figure out is...
If a block of wood dropped from a tall building has reached a velocity of 78.4 m/s, how long has it been falling?
I just don't know how to figure it out? Can you explain please?
you know that gravity provides constant acceleration. That means the the velocity grows by the same amount in equal time periods.
That is why g = 9.8 m/s^2
That means g = (9.8m/s)/s
Or, v grows by 9.8 m/s every second.
So, if v=9.8t after t seconds, then you want t where
9.8t = 78.4
Not so hard now, eh?
Of course! To determine the time it takes for an object to reach a certain velocity while falling, we can use the basic formula for linear motion:
V = u + at
where:
- V is the final velocity (in this case, 78.4 m/s)
- u is the initial velocity (in this case, when the block of wood is dropped, it is 0 m/s)
- a is the acceleration (in this case, the acceleration due to gravity is approximately 9.8 m/s^2)
- t is the time (which we are trying to find)
Since we know the values of V, u, and a, we can rearrange the formula to solve for t:
t = (V - u) / a
Substituting the given values into the equation:
t = (78.4 m/s - 0 m/s) / 9.8 m/s^2
Simplifying the equation, we have:
t = 78.4 m/s / 9.8 m/s^2
Calculating the result:
t = 8 seconds
Therefore, it takes approximately 8 seconds for the block of wood to reach a velocity of 78.4 m/s while falling.