Given:
The initial velocity of the car is: u = 0 m/s
The final velocity of the car is: v = 23.4 m/s
The velocity of the car changes over the time t = 2.90 s
To find:
a) The magnitude of the car's acceleration
b) The time taken by a car to change its speed from 11.7 m/s to 23.4 m/s
Explanation:
The acceleration of the object is defined as the rate of change of its velocity.
a)
Mathematically the acceleration of the car is given as:
[tex]a=\frac{v_-u}{t}[/tex]Here, a is the acceleration of the car.
Substituting the values in the above equation, we get:
[tex]a=\frac{23.4\text{ m/s}-0\text{ m/s}}{2.90\text{ s}}=\frac{23.4\text{ m/s}}{2.90\text{ s}}=8.068\text{ m/s}^2\approx8.07\text{ m/s}^2[/tex]b)
The car accelerates uniformly, thus, the acceleration of the car when its velocity changes from zero to 23.4 m/s will remain the same.
Let w be the initial velocity. Thus,
w = 11.7 m/s
The time taken by the car to change its speed from 11.7 m/s to 23.4 m/s can be determined as:
[tex]\begin{gathered} a=\frac{u-w}{t} \\ \\ t=\frac{u-w}{a} \\ \\ t=\frac{23.4\text{ m/s}-11.7\text{ m/s}}{8.07\text{ m/s}^2} \\ \\ t=1.45\text{ s} \end{gathered}[/tex]