staring from rest, a 3.5 kg object is acted upon by an unbalanced force and acquires a speed of 14.0 m/s after moving a distance of 35 m. find (a) the acceleration of the object, (b) the unbalanced force acting on the object, and (c) the time it takes for the object to attain a speed of 14.0 m/s
starting from rest (0 m/s) means that the average speed is 7 m/s
so it takes 5 s to go 35 m
acceleration = velocity / time = 14 / 5
force = mass * accel = 3.5 * 14/5
How to solve this problem
To find the information requested, we can use the equations of motion:
(a) We can find the acceleration of the object using the equation:
\[v^2 = u^2 + 2as\]
Where:
- \(v\) is the final velocity of the object (14.0 m/s),
- \(u\) is the initial velocity of the object (0 m/s, as it starts from rest),
- \(a\) is the acceleration of the object (to be found), and
- \(s\) is the distance traveled by the object (35 m).
Plugging in the values, we have:
\[14.0^2 = 0 + 2a \cdot 35\]
Simplifying the equation:
\[a = \frac{196.0}{70} = 2.8 \, \text{m/s}^2\]
(b) To find the unbalanced force acting on the object, we can use Newton's second law of motion:
\[F = ma\]
Where:
- \(F\) is the unbalanced force (to be found),
- \(m\) is the mass of the object (3.5 kg), and
- \(a\) is the acceleration of the object (2.8 m/s^2, as previously calculated).
Plugging in the values, we have:
\[F = 3.5 \times 2.8 = 9.8 \, \text{N}\]
(c) To find the time it takes for the object to attain a speed of 14.0 m/s, we can use the equation:
\[v = u + at\]
Where:
- \(t\) is the time taken for the object to attain the final velocity of 14.0 m/s (to be found).
Rearranging the equation, we get:
\[t = \frac{v - u}{a}\]
Plugging in the values, we have:
\[t = \frac{14.0 - 0}{2.8} = 5.0 \, \text{s}\]
Therefore, the answers to the given questions are:
(a) The acceleration of the object is 2.8 m/s^2,
(b) The unbalanced force acting on the object is 9.8 N,
(c) The time it takes for the object to attain a speed of 14.0 m/s is 5.0 s.
To find the answers to these questions, we can use the equations of motion.
(a) To find the acceleration of the object, we can use the equation:
v^2 = u^2 + 2as
where:
v = final velocity of the object (14.0 m/s)
u = initial velocity of the object (0 m/s since the object starts from rest)
a = acceleration of the object
s = distance traveled by the object (35 m)
Plugging in the values, we get:
14.0^2 = 0^2 + 2a * 35
Simplifying the equation, we have:
196 = 2a * 35
Dividing both sides by 70, we find:
a = 2.8 m/s^2
So, the acceleration of the object is 2.8 m/s^2.
(b) To find the unbalanced force acting on the object, we can use Newton's second law of motion:
F = ma
where:
F = force acting on the object
m = mass of the object (3.5 kg)
a = acceleration of the object (2.8 m/s^2)
Plugging in the values, we have:
F = 3.5 kg * 2.8 m/s^2
Simplifying the equation, we find:
F = 9.8 N
So, the unbalanced force acting on the object is 9.8 N.
(c) To find the time it takes for the object to attain a speed of 14.0 m/s, we can use the equation:
v = u + at
where:
v = final velocity of the object (14.0 m/s)
u = initial velocity of the object (0 m/s)
a = acceleration of the object (2.8 m/s^2)
t = time taken
Plugging in the values, we have:
14.0 = 0 + 2.8t
Simplifying the equation, we find:
2.8t = 14.0
Dividing both sides by 2.8, we get:
t = 5.0 s
So, the time it takes for the object to attain a speed of 14.0 m/s is 5.0 seconds.