This problem states that a car travels 100 km w/ the first half ofthe trip trave

Question

This problem states that a car travels 100 km w/ the first half ofthe trip traveling at 40 km/h and the second half unknown. Inorder the get the Avg. Velocity of 50 km/h, how fast does the carhave to travel the last 50 km.

I would have thought using the formula Vavg =(1/2)(Vo + V), you could have got the answer 60km/h. The answer they got is 66.67 km/s.

Please explain how even using the known formula above (for checkingthe answer) that still that the answer is 66.67 km/s.

Vavg = (1/2)(Vo + V) = (1/2)(40km/h + 66.67km/h) =53.335 km/h NOT 50km/h.

BUT

Explanation / Answer

The reason that the velocity equation that you tried to use isincorrect is because that assumes that the same amount of time isspent at each speed. Since this problem is talking about thelast 50 km, the equation would only be correct if the car spendsjust as much time on the second half, which would mean the samespeed. To correctly solve this problem just resort to the basicdeffinition of velocity vave=dnet/t t=dnet/vave =100/50=2 hr using the same equation you'll find that the first part of thetrip t=50/40= 1.25 hours leaving 0.75 hours for the last 50km. So: v=d/t =50/0.75 =66.67km/hr =100/50=2 hr using the same equation you'll find that the first part of thetrip t=50/40= 1.25 hours leaving 0.75 hours for the last 50km. So: v=d/t =50/0.75 =66.67km/hr

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