A car applies braking acceleration of 12.8 m/s (WEST). It takes a displacement of 813.0 m (EAST) for the car to come to rest. What was the inital velocity when the brakes were applied?
A car applies braking acceleration of 12.8 m/s (WEST). It takes a displacement of 813.0 m (EAST) for the car to come to rest. What was the inital velocity when the brakes were applied?
Answer:
We can use the kinematic equation that relates displacement, initial velocity, final velocity, acceleration, and time to solve this problem.
The equation is:
displacement = (initial velocity x time) + (0.5 x acceleration x time^2)
At the moment the car comes to rest, the final velocity is zero, so we can simplify the equation to:
displacement = (initial velocity x time) + (0.5 x acceleration x time^2) becomes displacement = (initial velocity x time) + (0.5 x acceleration x time^2) 813.0 m = (initial velocity x t) + (0.5 x (-12.8 m/s^2) x t^2) where we have used the negative sign for acceleration to indicate that it acts in the opposite direction to the displacement.
We need to find the initial velocity, which is the unknown in this equation. We can rearrange the equation to solve for it:
initial velocity = (displacement - 0.5 x acceleration x time^2) / time
Plugging in the given values, we get:
initial velocity = (813.0 m - 0.5 x (-12.8 m/s^2) x (t^2)) / t
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