To determine the acceleration of the car, we use the formula for acceleration, which is defined as the change in velocity divided by the time interval over which the change occurs. Mathematically, this is represented as:
[tex]\[ a = \frac{\Delta v}{\Delta t} \][/tex]
where [tex]\( a \)[/tex] is the acceleration, [tex]\( \Delta v \)[/tex] is the change in velocity, and [tex]\( \Delta t \)[/tex] is the time interval.
Step-by-Step Solution:
1. Identify the initial velocity ([tex]\( v_i \)[/tex]):
The initial velocity of the car is given as [tex]\( 35 \, \text{m/s} \)[/tex].
2. Identify the final velocity ([tex]\( v_f \)[/tex]):
The final velocity of the car is given as [tex]\( 65 \, \text{m/s} \)[/tex].
3. Determine the change in velocity ([tex]\( \Delta v \)[/tex]):
The change in velocity is the difference between the final velocity and the initial velocity:
[tex]\[ \Delta v = v_f - v_i = 65\, \text{m/s} - 35\, \text{m/s} = 30\, \text{m/s} \][/tex]
4. Identify the time interval ([tex]\( \Delta t \)[/tex]):
The time interval over which this change occurs is given as [tex]\( 5 \)[/tex] seconds.
5. Calculate the acceleration ([tex]\( a \)[/tex]):
Substitute the values of [tex]\( \Delta v \)[/tex] and [tex]\( \Delta t \)[/tex] into the acceleration formula:
[tex]\[ a = \frac{\Delta v}{\Delta t} = \frac{30 \, \text{m/s}}{5 \, \text{s}} = 6 \, \text{m/s}^2 \][/tex]
Therefore, the acceleration of the car is [tex]\( 6 \, \text{m/s}^2 \)[/tex].
Conclusion:
The correct option is:
[tex]\[ \boxed{6 \, \text{m/s}^2} \][/tex]
