A certain car is capable of accelerating at a uniform rate of .94m/s^2. What is the magnitude of the car's displacement as it accelerates uniformly from a speed of 87km/h to one of 97km/h? Answer in units of m.
To find the displacement of the car, we need to use the equations of motion for uniformly accelerated motion. The key equation we will use is:
v^2 = u^2 + 2as
where:
- v is the final velocity,
- u is the initial velocity,
- a is the acceleration, and
- s is the displacement.
First, convert the initial and final velocities from km/h to m/s.
Initial velocity (u) = 87 km/h = (87 * 1000) / 3600 m/s
Final velocity (v) = 97 km/h = (97 * 1000) / 3600 m/s
Next, we calculate the acceleration (a) using the given information of uniform acceleration:
a = 0.94 m/s^2
Now we have the values for u, v, and a, and we need to find s. Rearranging the equation,
s = (v^2 - u^2) / (2a)
Substitute the known values into the equation:
s = ((97 * 1000/3600)^2 - (87 * 1000/3600)^2) / (2 * 0.94)
Now we can calculate the value of s.