The gauge pressure in the tires of your car is 210 kPa (30.5 psi) when the temperature is 25°C (77 °F). Several days later it is
1 answer:
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Answer:
v = (-4.44 i^ + 6.66 j^ ) m/s, a_average =( 0 i^ -2π j^) m/s²
Explanation:
The expression left corresponds to an oscillatory movement (MAS), the speed is defined by
v = dr / dt
the function of position
r = 2 cos πt i^ + 3 sin πt j^
let us note that it is a movement in two dimensions
let's perform the derivative
v = -2π sin πt i^ + 3π cos πt j^
we evaluate this expression for t = 0.25 s, remember that the angle is in radians
v = -2π sin (π 0.25) i^ + 3π cos (π 0.25) j^
v = (-4.44 i^ + 6.66 j^ ) m/s
To calculate the mean acceleration we use the expression
a = () / Δt
indicates that the time is the first 3 s
we look for the initial velocity t = 0 s
v₀ = 0 i ^ + 3π j ^
we look for the fine velocity, t = 3 s
v_f = - 2π sin (π 3) + 3π cos (π 3) j ^
v_f = 0 i ^ - 3π j ^
we calculate the average acceleration
Δt = (3 -0) = 3 s
a_average = (0-0) / 3 i ^ + (-3π - 3π) / 3
a_average = (0 i ^ -2π j ^ ) m/s²
Answer:
(a) The announcer's claim is incorrect because the divers enter at a speed of 20.4 and not 25 m/s as announced
(b) it’s possible for a diver to enter the water with the velocity of 25 m/s if he has initial velocity of 14.4 m/s. The upward initial velocity can’t be physically attained
Explanation:
(a)
To find the final velocity for an object traveling distance h taking the initial vertical component of velocity as
the kinematics equation is written as
where a is acceleration
Substituting g for a where g is gravitational force value taken as 9.81
Since the initial velocity is zero, we can solve for final velocity by substituting figures, note that 70 ft is 21.3 m for h
= 20.44275
Therefore, the divers enter with a speed of 20.4 m/s
The announcer's claim is incorrect because the divers enter at a speed of 20.4 and not 25 m/s as announced
(b)
The divers can enter water with a velocity of 25 m/s only if they have some initial velocity. Using the kinematic equation
Since we have final velocity of 25 m/s
= 14.390761 m/s
Therefore, it’s possible for a diver to enter the water with the velocity of 25 m/5 if he has initial velocity of 14.4 m/s
In conclusion, the upward initial velocity can’t be physically attained