a car is accelerating at a uniform rate of 0.85 m/s^2. what is the magnitude of the car's displacement as it accelerates uniformly from a speed of 83 km/h to one of 94 km/h?
i tried a formula that solves for displacement and uses initial and final velocity and acceleration..i got something like 1.28, but the real answer is 88 m
please tell me how to solve for this
Vf^2=Vi^2 + 2*acceleration * distance.
Did you change km/h to m/s?
No. How can you change 94 km/h to m/s?
1 km/h = 1000m/3600s = ________ m/s
Now you should be able to do the conversion for 94 km/h
To solve for the magnitude of the car's displacement as it accelerates uniformly, you can use the following steps:
Step 1: Convert the initial and final velocities from km/h to m/s:
- Initial velocity (u) = 83 km/h = 83 * (1000 m/1 km) * (1 h/3600 s) = 23.05 m/s
- Final velocity (v) = 94 km/h = 94 * (1000 m/1 km) * (1 h/3600 s) = 26.11 m/s
Step 2: Find the change in velocity (Δv) by subtracting the initial velocity from the final velocity:
- Δv = v - u = 26.11 m/s - 23.05 m/s = 3.06 m/s
Step 3: Use the equation of motion for uniformly accelerated motion:
- Displacement (s) = (v^2 - u^2) / (2a), where a is the acceleration
Step 4: Substitute the values into the equation to calculate the displacement:
- s = (26.11^2 - 23.05^2) / (2 * 0.85) = (681.9721 - 531.3025) / 1.7 = 150.6696 / 1.7 = 88.63 m
Therefore, the magnitude of the car's displacement as it accelerates uniformly from a speed of 83 km/h to one of 94 km/h is approximately 88 meters. The difference in your result might be due to rounding errors during the calculations.