To determine how long it will take for a car to accelerate from a speed of \( 20.0 \, \text{m/s} \) to a speed of \( 25.0 \, \text{m/s} \) with an acceleration of \( 3.0 \, \text{m/s}^2 \), we can use the basic kinematic equation that relates speed, acceleration, and time:
[tex]\[
\text{final speed} = \text{initial speed} + (\text{acceleration} \times \text{time})
\][/tex]
Rearranging this formula to solve for time (\( t \)), we get:
[tex]\[
t = \frac{\text{final speed} - \text{initial speed}}{\text{acceleration}}
\][/tex]
Let's plug in the values given:
- Initial speed (\( v_i \)) = \( 20.0 \, \text{m/s} \)
- Final speed (\( v_f \)) = \( 25.0 \, \text{m/s} \)
- Acceleration (\( a \)) = \( 3.0 \, \text{m/s}^2 \)
Substitute these values into the formula:
[tex]\[
t = \frac{25.0 \, \text{m/s} - 20.0 \, \text{m/s}}{3.0 \, \text{m/s}^2}
\][/tex]
Calculate the difference in speeds:
[tex]\[
25.0 \, \text{m/s} - 20.0 \, \text{m/s} = 5.0 \, \text{m/s}
\][/tex]
Now, divide this by the acceleration:
[tex]\[
t = \frac{5.0 \, \text{m/s}}{3.0 \, \text{m/s}^2} = 1.\overline{6} \, \text{s}
\][/tex]
Therefore, the time required for the car to go from [tex]\( 20.0 \, \text{m/s} \)[/tex] to [tex]\( 25.0 \, \text{m/s} \)[/tex] is approximately [tex]\( 1.67 \)[/tex] seconds, which can be represented more precisely as [tex]\( 1.6666666666666667 \)[/tex] seconds.
