Answer:
Final speed of the car, v = 24.49 m/s
Explanation:
It is given that,
Initial velocity of the car, u = 0
Acceleration,
Time taken, t = 7.9 s
We need to find the final velocity of the car. Let it is given by v. It can be calculated using first equation of motion as :
v = 24.49 m/s
So, the final speed of the car is 24.49 m/s. Hence, this is the required solution.
Answer:
v = 0.84m/s, v(max)= 0.997m/s
Explanation:
Initial work done by the spring, where c is the compression = 0.28m:
Work lost to friction:
Energy:
(a) Solve for v:
(b) Solve for x:
if:
The working equation for this problem is written below:
x = v₀t + 0.5at², where x is the distance traveled, v₀ is the initial velocity, a is the acceleration and t is the time
Let's apply the concept of calculus. The maximum speed is equated to the derivative of x with respect to t.
dx/dt = 8 ft/s = v₀ + at
Since the it starts from rest, v₀ = 0
8 = at
t = 8/a
The net acceleration is 0.7 - 0.35 = 0.35 ft/s². Thus,
t = 8/0.35 = 22.86 seconds
Answer:
the period of the motion will increase by√2.
Explanation:
Given that the motion you are talking about is circular motion of a mass attached to the end of a string. I speculated that from the word usage in the question(e.g radius instead of length, tension, period). Given this is so we will have to recall the formula for the centripetral force Fc acting on the object which will be equal in magnitude to the tension in the string and will be given by,
if we want the above defined tension to remain constant when we double the mass and keep the radius of the string constant, the the w(angular frequency) must change which is related to the period by the below equation which will also change,
to find out by how much the period will change we see that from the first equation that if we double the mass making it 2m then the <em>w</em>² will have to decrease by 2 that is it will become <em>w</em>²/2, at the same time keeping r constant since it says that in the question. We now absorb the 2 inside the square and we get,
we can clearly see that the new period has become,
where T is the old period. So the new period is √2 times the old period given by the equation above.