Answer :
To find out how fast the cart was rolling away, we can use the impulse-momentum formula. According to this formula:
[tex]\[ F \times t = m \times \Delta v \][/tex]
Where:
- [tex]\( F \)[/tex] is the force applied (in Newtons)
- [tex]\( t \)[/tex] is the time duration over which the force is applied (in seconds)
- [tex]\( m \)[/tex] is the mass of the cart (in kilograms)
- [tex]\( \Delta v \)[/tex] is the change in velocity (in meters per second)
Given values are:
- Force ([tex]\( F \)[/tex]): 9.0 N
- Time ([tex]\( t \)[/tex]): 8.00 seconds
- Mass ([tex]\( m \)[/tex]): 41.5 kg
We need to solve for the change in velocity ([tex]\( \Delta v \)[/tex]):
1. Calculate the change in velocity:
[tex]\[
\Delta v = \frac{F \times t}{m}
\][/tex]
2. Substitute the given values:
[tex]\[
\Delta v = \frac{9.0 \, \text{N} \times 8.00 \, \text{s}}{41.5 \, \text{kg}}
\][/tex]
3. Perform the multiplication in the numerator:
[tex]\[
9.0 \, \text{N} \times 8.00 \, \text{s} = 72.0 \, \text{Ns}
\][/tex]
4. Divide by the mass:
[tex]\[
\Delta v = \frac{72.0 \, \text{Ns}}{41.5 \, \text{kg}}
\][/tex]
5. Calculate the result:
[tex]\[
\Delta v \approx 1.73 \, \text{m/s}
\][/tex]
The closest listed option to this calculated change in velocity is [tex]\( 1.7 \, \text{m/s} \)[/tex]. Thus, the cart was initially rolling away approximately at a speed of [tex]\( 1.7 \, \text{m/s} \)[/tex].
[tex]\[ F \times t = m \times \Delta v \][/tex]
Where:
- [tex]\( F \)[/tex] is the force applied (in Newtons)
- [tex]\( t \)[/tex] is the time duration over which the force is applied (in seconds)
- [tex]\( m \)[/tex] is the mass of the cart (in kilograms)
- [tex]\( \Delta v \)[/tex] is the change in velocity (in meters per second)
Given values are:
- Force ([tex]\( F \)[/tex]): 9.0 N
- Time ([tex]\( t \)[/tex]): 8.00 seconds
- Mass ([tex]\( m \)[/tex]): 41.5 kg
We need to solve for the change in velocity ([tex]\( \Delta v \)[/tex]):
1. Calculate the change in velocity:
[tex]\[
\Delta v = \frac{F \times t}{m}
\][/tex]
2. Substitute the given values:
[tex]\[
\Delta v = \frac{9.0 \, \text{N} \times 8.00 \, \text{s}}{41.5 \, \text{kg}}
\][/tex]
3. Perform the multiplication in the numerator:
[tex]\[
9.0 \, \text{N} \times 8.00 \, \text{s} = 72.0 \, \text{Ns}
\][/tex]
4. Divide by the mass:
[tex]\[
\Delta v = \frac{72.0 \, \text{Ns}}{41.5 \, \text{kg}}
\][/tex]
5. Calculate the result:
[tex]\[
\Delta v \approx 1.73 \, \text{m/s}
\][/tex]
The closest listed option to this calculated change in velocity is [tex]\( 1.7 \, \text{m/s} \)[/tex]. Thus, the cart was initially rolling away approximately at a speed of [tex]\( 1.7 \, \text{m/s} \)[/tex].