Answer:
Average velocity v = 21.18 m/s
Average acceleration a = 2 m/s^2
Explanation:
Average speed equals the total distance travelled divided by the total time taken.
Average speed v = ∆x/∆t = (x2-x1)/(t2-t1)
Average acceleration equals the change in velocity divided by change in time.
Average acceleration a = ∆v/∆t = (v2-v1)/(t2-t1)
Where;
v1 and v2 are velocities at time t1 and t2 respectively.
And x1 and x2 are positions at time t1 and t2 respectively.
Given;
t1 = 3.0s
t2 = 20.0s
v1 = 11 m/s
v2 = 45 m/s
x1 = 25 m
x2 = 385 m
Substituting the values;
Average speed v = ∆x/∆t = (x2-x1)/(t2-t1)
v = (385-25)/(20-3)
v = 21.18 m/s
Average acceleration a = ∆v/∆t = (v2-v1)/(t2-t1)
a = (45-11)/(20-3)
a = 2 m/s^2
Answer:
75.71 m/s
Explanation:
From equation of motion, acceleration is given by
where v is the final velocity, u is the initial velocity and t is time taken.
Making v the subject of the above formula
v=at+u
Substituting 6.7 s for time, t and 11.3 for a and taking u as zero since it starts from rest
v=11.3*6.7=75.71 m/s
Answer:
454,320 joules
Explanation:
The work done on an object is equal to its change in kinetic energy: Change in KE = F × d.
Plug the values for F and d into the formula and solve:
Change in KE = 2,524 × 180
= 454,320 joules
The roller coaster gains 454,320 joules of energy from the work done on it by the chain.
Answer:
The first harmonic is: 250Hz, second harmonic 500Hz, third harmonic 750Hz.
Explanation:
Use the frequency f, speed v, and wavelentgh L relationship:

We are given the speed v=400 m/s. The base wavelength on a string of length 80cm is twice the length of the string (a "half wave" along the full length of the string), so:

The fundamental frequency (first harmonic) is 250 Hz
The second harmonic is produced by one full wave across the string (adding one node in the middle), so L=80cm in this case, therefore the second harmonic frequency is: f2 = 2*250=500Hz
the third harmonic add another node (and a half wave) to the pattern and the wavelength will be 2/3 of 80cm, so f3=3*250Hz = 750Hz