To determine how long it will take for a car starting from rest to reach a speed of 20 meters per second with a constant acceleration of 4 meters per second squared, we can use the first equation of motion:
[tex]\[ v = u + at \][/tex]
where:
- [tex]\( v \)[/tex] is the final velocity (20 m/s in this case),
- [tex]\( u \)[/tex] is the initial velocity (0 m/s since the car starts from rest),
- [tex]\( a \)[/tex] is the acceleration (4 m/s²),
- [tex]\( t \)[/tex] is the time we need to find.
Step-by-step, it works as follows:
1. Plug in the known values:
[tex]\[ 20 = 0 + 4t \][/tex]
2. Simplify the equation:
[tex]\[ 20 = 4t \][/tex]
3. Solve for [tex]\( t \)[/tex] by dividing both sides by 4:
[tex]\[ t = \frac{20}{4} \][/tex]
4. This gives:
[tex]\[ t = 5 \text{ seconds} \][/tex]
Thus, it will take the car 5 seconds to reach a speed of 20 m/s. Therefore, the correct answer is:
5 sec
