Answer :
Sure! Here's how you can solve this problem step-by-step:
1. Identify the given information:
- Mass of the car ([tex]\( m \)[/tex]) = 1330 kg
- Force applied ([tex]\( F \)[/tex]) = 187 N
- Distance to move the car ([tex]\( d \)[/tex]) = 5.00 m
- Initial velocity ([tex]\( v_0 \)[/tex]) = 0 (since the car is initially at rest)
2. Calculate the acceleration:
- Use Newton's second law of motion, [tex]\( F = ma \)[/tex], where [tex]\( a \)[/tex] is the acceleration.
- Rearrange to solve for acceleration: [tex]\( a = \frac{F}{m} \)[/tex].
[tex]\[
a = \frac{187 \, \text{N}}{1330 \, \text{kg}} \approx 0.1406 \, \text{m/s}^2
\][/tex]
3. Find the time taken to move the car 5.00 meters:
- Use the kinematic equation for motion with constant acceleration, [tex]\( d = v_0 t + \frac{1}{2} a t^2 \)[/tex].
- Since the initial velocity [tex]\( v_0 \)[/tex] is 0, the equation simplifies to [tex]\( d = \frac{1}{2} a t^2 \)[/tex].
- Rearrange to solve for time [tex]\( t \)[/tex]: [tex]\( t = \sqrt{\frac{2d}{a}} \)[/tex].
[tex]\[
t = \sqrt{\frac{2 \times 5.00 \, \text{m}}{0.1406 \, \text{m/s}^2}} \approx 8.43 \, \text{s}
\][/tex]
4. Conclusion:
- The car takes approximately 8.43 seconds to move 5.00 meters when a force of 187 N is applied.
So, the time it takes for the car to move 5.00 meters is about 8.43 seconds.
1. Identify the given information:
- Mass of the car ([tex]\( m \)[/tex]) = 1330 kg
- Force applied ([tex]\( F \)[/tex]) = 187 N
- Distance to move the car ([tex]\( d \)[/tex]) = 5.00 m
- Initial velocity ([tex]\( v_0 \)[/tex]) = 0 (since the car is initially at rest)
2. Calculate the acceleration:
- Use Newton's second law of motion, [tex]\( F = ma \)[/tex], where [tex]\( a \)[/tex] is the acceleration.
- Rearrange to solve for acceleration: [tex]\( a = \frac{F}{m} \)[/tex].
[tex]\[
a = \frac{187 \, \text{N}}{1330 \, \text{kg}} \approx 0.1406 \, \text{m/s}^2
\][/tex]
3. Find the time taken to move the car 5.00 meters:
- Use the kinematic equation for motion with constant acceleration, [tex]\( d = v_0 t + \frac{1}{2} a t^2 \)[/tex].
- Since the initial velocity [tex]\( v_0 \)[/tex] is 0, the equation simplifies to [tex]\( d = \frac{1}{2} a t^2 \)[/tex].
- Rearrange to solve for time [tex]\( t \)[/tex]: [tex]\( t = \sqrt{\frac{2d}{a}} \)[/tex].
[tex]\[
t = \sqrt{\frac{2 \times 5.00 \, \text{m}}{0.1406 \, \text{m/s}^2}} \approx 8.43 \, \text{s}
\][/tex]
4. Conclusion:
- The car takes approximately 8.43 seconds to move 5.00 meters when a force of 187 N is applied.
So, the time it takes for the car to move 5.00 meters is about 8.43 seconds.
