An automobile accelerates 1.24 m/s^2 over 6.00 s to reach freeway speed at the end of an entrance ramp. If the cars final speed is 86.0 km/h, what was its initial speed when it began accelerating? Express your answer in km/h I can do it but I just don't know how I'm supposed to put it in km/h
To solve this problem, we can use the formula for acceleration:
Final velocity = Initial velocity + (acceleration × time)
We are given:
Acceleration (a) = 1.24 m/s^2
Time (t) = 6.00 s
Final velocity (Vf) = 86.0 km/h
First, let's convert the final velocity from km/h to m/s:
86.0 km/h = 86.0 × (1000 m/1 km) / (3600 s/1 h) = 23.89 m/s
Now, we substitute the known values into the formula to solve for the initial velocity (Vi):
23.89 m/s = Vi + (1.24 m/s^2 × 6.00 s)
Next, rearrange the equation to solve for Vi:
Vi = 23.89 m/s - (1.24 m/s^2 × 6.00 s)
Vi = 23.89 m/s - 7.44 m/s
Vi = 16.45 m/s
Finally, let's convert the initial velocity back to km/h by multiplying by (3600 s/1 h) and dividing by (1000 m/1 km):
Vi = 16.45 × (3600/1000) km/h ≈ 59.22 km/h
Therefore, the initial speed of the car when it began accelerating was approximately 59.22 km/h.