Answer:
a = 0.7267
, acceleration is positive therefore the speed is increasing
Explanation:
The definition of acceleration is
a = dv / dt
they give us the function of speed
v = - (t-1) sin (t² / 2)
a = - sin (t²/2) - (t-1) cos (t²/2) 2t / 2
a = - sin (t²/2) - t (t-1) cos (t²/2)
the acceleration for t = 4 s
a = - sin (4²/2) - 4 (4-1) cos (4²/2)
a = -sin 8 - 12 cos 8
remember that the angles are in radians
a = 0.7267
the problem does not indicate the units, but to be correct they must be m/s²
We see that the acceleration is positive therefore the speed is increasing
Ah hah ! Thank you for that data at the end ... about the 2.5kg box.
I thought we were going to have to calculate it from Square-1.
Without checking, I'll assume that a 2.5kg box at that location really
does weigh 6.1 Newtons.
Weight (gravitational force) is directly proportional to the mass of
the object ... if you eat twice as much, you'll weigh twice as much.
So the weight of the 1kg box is
(1 / 2.5) x (6.1 N) = 2.44 Newtons .
(1) The time taken for the drag racer to accelerate is 4.89 s
(2) The speed of the contestant (a) in feet per second is 30.89 ft/s (b) in miles per hr is 21.12 miles per hr.
(1) To calculate the time required to accelerate 18 ft/sec² from rest to a velocity of 60 mph, we use the formula below.
Formula:
- t = (v-u)/a........... Equation 1
Where:
- t = time
- v = Final velocity
- u = initial velocity
- a = acceleration.
From the question,
Given:
- a = 18 ft/sec² = (18×0.3048) = 5.4864 m/s²
- v = 60 mph = (60×0.44704) = 26.82 m/s
- u = 0 m/s ( from rest)
Substitute these values into equation 1
- t = (26.82-0)/5.4864
- t = 4.89 seconds
(2) To calculate the speed of the contestant, we use the formula below
Formula:
- s = d/t............ Equation 1
Where:
- s = speed of the contestant
- d = distance
- t = time.
From the question,
Given:
Substitute these values into equation 1
(a) In feet = (9.43/0.3048) = 30.94 ft/s
(b) in miles per hr = (9.43×2.24) = 21.12 miles per hr
Hence, (1) The time taken for the drag racer to accelerate is 4.89 s (2) The speed of the contestant (a) in feet per second is 30.89 ft/s (b) in miles per hr is 21.12 miles per hr.
Learn more about speed here: brainly.com/question/4931057
The rate of change of velocity