A certain car is capable of accelerating at a
uniform rate of 0.82 m/s2.
What is the magnitude of the car’s displace-
ment as it accelerates uniformly from a speed
of 85 km/h to one of 95 km/h?
Answer in units of m.
The 10 km/h velocity change is 2.78 m/s
The time required to accomplish that velocity change is (deltaV)/a
= (2.78 m/s)/0.82 m/s^2 = 3.39 s
The displacement will be the average velocity multiplied by that time.
X = (90 km/h)*3.39 s* 1h/3600 s
= ___ meters
To find the displacement of the car, we can use the formula:
displacement = final velocity - initial velocity
First, let's convert the initial velocity from km/h to m/s:
initial velocity = 85 km/h = (85 * 1000 m) / (3600 s) ≈ 23.61 m/s
Next, let's convert the final velocity from km/h to m/s:
final velocity = 95 km/h = (95 * 1000 m) / (3600 s) ≈ 26.39 m/s
Now we can calculate the displacement:
displacement = final velocity - initial velocity
= 26.39 m/s - 23.61 m/s
≈ 2.78 m
Therefore, the magnitude of the car's displacement as it accelerates from 85 km/h to 95 km/h is approximately 2.78 m.
To find the displacement of the car, you need to calculate the change in velocity. First, convert the initial and final velocities from km/h to m/s.
Initial velocity = 85 km/h
Final velocity = 95 km/h
Conversion:
1 km/h = 0.2778 m/s
Initial velocity (v1) = 85 km/h * 0.2778 m/s = 23.6111 m/s
Final velocity (v2) = 95 km/h * 0.2778 m/s = 26.3889 m/s
Next, calculate the change in velocity (Δv) by subtracting the initial velocity from the final velocity.
Δv = v2 - v1 = 26.3889 m/s - 23.6111 m/s = 2.7778 m/s
Now, since the car is accelerating uniformly, you can use the formula for displacement to find the answer:
Displacement (Δx) = (v2^2 - v1^2) / (2a)
where a is the acceleration.
Substituting the values we have:
Δx = (26.3889^2 m/s - 23.6111^2 m/s) / (2 * 0.82 m/s^2)
Calculating this expression will give you the magnitude of the car's displacement as it accelerates from 85 km/h to 95 km/h.