A rock is dropped from a bridge into the water below. If it falls for 2.00 seconds, what is its average velocity? What is its instantaneous velocity?
after falling for 2 s ... the impact velocity is .... 2.00 s * g = 18.6 m/s
the average velocity is half of the impact velocity ... 9.81 m/s
the 2 makes things fairly simple
2g = 19.6
a = -9.81 m/s^2
a is acceleration due to gravity
v = Vi - 9.81 t
v is velocity, Vi is initial velocity, zero if dropped
so here v = -9.81 t m/s
at t = 2 seconds, v = 9.81*2 = 19.62 meters/second at ground
is is linear in t and v goes from 0 to 19.62 in 2 seconds so
v average = (0 + 19.62)/2 = 9.81 m/s
To go on with problem:
h = Hi + Vi t - (9.81/2 )t^2
h is height in meters, Hi is initial height. t is 2 seconds
so here 0 = Hi + 0 - 4.9*2^2
so
0 = Hi - 4.9 * 4
Hi = 19.6 meters initial height
oops ... math error
To find the average velocity of the rock, we need to know the total distance it fell during the 2.00 seconds.
The average velocity (v_avg) is given by the formula: v_avg = Δd / Δt
where Δd is the change in distance and Δt is the change in time.
In this case, the rock is dropped vertically, so we can assume its initial velocity is 0 m/s. The only force acting on the rock is gravity, pulling it downward. Therefore, the rock experiences constant acceleration due to gravity (g) of approximately 9.8 m/s².
We can use the kinematic equation to find the distance (d) fallen by the rock:
d = 1/2 * g * t^2
where t is the time in seconds and g is the acceleration due to gravity.
So, for the given time of 2.00 seconds, we have:
d = 1/2 * 9.8 m/s² * (2.00 s)^2
Now, we can substitute the calculated value of d into the average velocity formula:
v_avg = d / t
To find the instantaneous velocity at any given point during the motion, you can use calculus or an approximation method. However, since the rock is being dropped vertically with constant acceleration due to gravity, its instantaneous velocity will increase linearly with time. So, at the instant of 2.00 seconds, the instantaneous velocity is equal to the average velocity.
Hence, to find the average velocity, we can use the formula:
v_avg = d / t, with d calculated as shown above.