What force is required to accelerated a body with a mass of 15 kilograms at a rate of 8 m/s2
1 answer:
You might be interested in
Answer:
1) No, the car does not travel at constant speed.
2) V = 9 ft/s
3) No, the car does not travel at constant speed.
4) V = 5.9 ft/s
Explanation:
In order to know if the car is traveling at constant speed we need to derive the given formula. That way we get speed as a function of time:
V(t) = 2*t + 2 Since the speed depends on time, the speed is not constant at any time.
For the average speed we evaluate the formula for t=2 and t=5:
d(2) = 8 ft and d(5) = 35 ft
Again, for the average speed we evaluate the formula for t=1.8 and t=2.1:
d(1.8) = 6.84 ft and d(2.1) = 8.61 ft
Answer:
b) a = -k / m x , c) d²x / dt² = - A w² cos (wt+Ф) , d) and e) T = 2π √m / k
h) a = - A w² cos (wt+Ф)
Explanation:
a) see free body diagram in the attachment
b) We write Newton's second law
Fe = m a
-k x = ma
a = -k / m x
c) the acceleration is
a = d²x / dt²
If x = A cos wt
v = dx / dt = -A w sin (wt +Ф)
a = d²x / dt² = - A w² cos (wt+Ф)
d) we substitute in Newton's second law
d²x / dt² = -k / m x
We call
w² = k / m
e) substitute to find w
-A w² cos (wt+Ф) = -k / m A cos (wt+Ф)
w² = k / m
Angular velocity and frequency are related
w = 2π f
f = 1 / T
We substitute
T = 2π / w
T = 2π √m / k
g) v= - A w sin (wt+Ф)
h) acceleration is
a = - A w² cos (wt+Ф)
