Final answer:
The acceleration of a car that increases its speed from rest to 60 m/s while covering a distance of 90 m is calculated using the kinematic equation v^2 = u^2 + 2as. By substituting the given values, the car's acceleration is found to be 20 m/s^2.
Step-by-step explanation:
To calculate the acceleration of a car that goes from rest to 60 m/s and covers a distance of 90 m, we can use one of the kinematic equations that relate acceleration, final velocity, initial velocity, distance, and time. The appropriate kinematic equation for this scenario, where initial velocity (u) is 0 (since the car starts from rest), final velocity (v) is 60 m/s, and distance (s) is 90 m, is:
v^2 = u^2 + 2as
We can rearrange this to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Plugging in the values:
a = (60^2 - 0^2) / (2 * 90)
a = 3600 / 180
a = 20 m/s^2
Therefore, the car's acceleration is 20 m/s^2.