A car drives down the highway at a constant speed. The speed limit increases and the car accelerates to 35 m/s in 4.5 seconds over a displacement of 100 m. What is the cars acceleration.
v = vo + at
s = vo*t + 1/2 at^2
vo + a*4.5 = 35
vo*4.5 + 1/2 a*4.5^2 = 100
so,
(35-4.5a)(4.5) + 1/2 a * 4.5^2 = 100
a = 5.68 m/s^2
To find the acceleration, we can use the formula:
acceleration = change in velocity / time
In this case, the change in velocity is the final velocity minus the initial velocity. As mentioned in the question, the initial velocity is not given, but we know that the car accelerates to a final velocity of 35 m/s. Therefore, the change in velocity is 35 m/s minus the initial velocity.
We are also given the time it takes for the car to reach this final velocity, which is 4.5 seconds. Therefore, the equation becomes:
acceleration = (35 m/s - initial velocity) / 4.5 seconds
To solve for the initial velocity, we need additional information.