A certain car is capable of accelerating at a uniform rate of 0.85 m/s2. 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 don't get this question. How do you calculate displacement without the time? Thnx in advance.
vf^2=vi^2 + 2*acceleration*displacement
To calculate the displacement without knowing the time, we can use the following equation:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
In this case, the initial velocity (u) is 83 km/h, which can be converted to m/s:
u = 83 km/h * (1000 m/km) / (3600 s/h) ≈ 23.06 m/s
The final velocity (v) is 94 km/h, which can also be converted to m/s:
v = 94 km/h * (1000 m/km) / (3600 s/h) ≈ 26.11 m/s
The acceleration (a) is given as 0.85 m/s^2.
Plugging these values into the equation, we have:
(26.11 m/s)^2 = (23.06 m/s)^2 + 2 * 0.85 m/s^2 * s
Simplifying the equation, we get:
681.57 m^2/s^2 = 531.8436 m^2/s^2 + 1.7 m/s^2 * s
Rearranging the equation, we have:
681.57 m^2/s^2 - 531.8436 m^2/s^2 = 1.7 m/s^2 * s
149.7264 m^2/s^2 = 1.7 m/s^2 * s
Dividing both sides by 1.7 m/s^2, we get:
s = 149.7264 m^2/s^2 / 1.7 m/s^2
s ≈ 88.07 meters
Therefore, the magnitude of the car's displacement is approximately 88.07 meters.
To calculate the displacement of the car without the time, we can use the equations of motion for uniformly accelerated motion.
In this case, the car is accelerating uniformly from an initial speed of 83 km/h to a final speed of 94 km/h. We need to convert these speeds to meters per second (m/s) to be consistent with the units of acceleration.
1 km/h is equal to 0.2778 m/s. So, the initial speed is 83 km/h * 0.2778 m/s = 23.05 m/s, and the final speed is 94 km/h * 0.2778 m/s = 26.11 m/s.
Now, let's use the equation of motion: v^2 = u^2 + 2as.
Where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- s is the displacement
Rearranging the equation to solve for s, we have:
s = (v^2 - u^2) / (2a)
Substituting the values:
s = (26.11^2 - 23.05^2) / (2 * 0.85)
s = (682.5921 - 531.8025) / 1.70
s = 150.7896 / 1.70
s = 88.7 meters
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 88.7 meters.