How Do You Calculate the Total Displacement of a Car Accelerating Uniformly?

[intenzxboi]

Homework Statement

If a car cruises at 11.3m/s for 75s, then uniformly speeds up until, after 45s, it reaches a speed of 18.5 m/s, what is the car's displacement during this motion?

Homework Equations

v(1)=at+v(o)
v^2=v(o)^2 +2a(x-xo)

The Attempt at a Solution

V(o)=11.3
V(1)=18.5
t=45

a=7.2/45=.16

so by plugging in all this values into v^2=v(o)^2 +2a(x-xo) i get 670.5m

But they are telling me the answer is 1.52km

 

[intenzxboi]

nm solved it.. its asking for the displacement of the whole trip..

man i hate how the questions are worded in a tricky way.

 

[thomate1]

I would approach this problem by first checking the given values to ensure they are accurate and consistent. The given values for initial and final velocities, as well as the time, seem reasonable. However, there is a discrepancy between the acceleration calculated using the given values and the acceleration given in the problem statement. The calculated acceleration is 0.16 m/s^2, while the given acceleration is 7.2 m/s^2. This could be a typo or a mistake in the calculation.

Assuming that the given acceleration is correct, the displacement can be calculated using the equations provided in the homework statement. Using the equation v(1) = at + v(0), we can solve for the displacement (x-x0) at t=45 seconds, which is the time when the car reaches its final velocity of 18.5 m/s. This gives us a displacement of 405.5 m.

To find the total displacement, we also need to consider the initial motion of the car at a constant velocity of 11.3 m/s for 75 seconds. Using the equation x = v(0)t, we can calculate the displacement during this initial motion, which is 847.5 m.

Therefore, the total displacement of the car during this motion is 405.5 m + 847.5 m = 1253 m, which is equivalent to 1.25 km. This is closer to the given answer of 1.52 km, but there may still be a slight discrepancy due to rounding errors or other factors. It is important to always double-check calculations and given values to ensure accuracy in scientific analysis.