A car that was initially at rest reaches a final speed of +50.0 m/s over a displacement of +55.0 m.
What is the magnitude of the acceleration?
Find the time it took to travel the first 55 m.
a=v²/2s=...
s=at²/2 =>
t=sqrt{2s/a)=...
I don't understand.. could you give a better answer?
To find the magnitude of acceleration, we can use the following equation:
Acceleration (a) = (Final velocity (v) - Initial velocity (u)) / Time taken (t)
Since the car was initially at rest, the initial velocity (u) is 0 m/s. The final velocity (v) is +50.0 m/s. We can rearrange the equation to solve for acceleration:
a = v / t
To find the time it took to travel the first 55 m, we can use the kinematic equation:
Displacement (s) = Initial velocity (u) * Time taken (t) + (0.5 * Acceleration (a) * Time taken (t)^2)
Since the initial velocity (u) is 0 m/s and the displacement (s) is +55.0 m, we can rearrange the equation to solve for time:
55.0 m = 0.5 * a * t^2
Let's solve these equations step by step:
1. Calculate the magnitude of acceleration (a):
a = v / t
a = 50.0 m/s / t
2. Find the time taken (t) using the equation for displacement:
55.0 m = 0.5 * a * t^2
110.0 m = a * t^2
Dividing both sides by a:
t^2 = 110.0 m / a
Taking the square root of both sides:
t = √(110.0 m / a)
Now, if you have a specific value for the acceleration (a), you can substitute it into the equation and calculate the time (t). If not, you will need additional information to determine the acceleration.